Subgroups — C₃×#3545 #87429

Order 384.

1060 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#562	C₂	1	2	yes	maximal, complemented
3	C₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#555	C₂	1	2	yes	maximal, complemented
5	C₃×#551	C₂	1	2	yes	maximal, complemented
6	C₃×#551	C₂	1	4	yes	maximal, complemented
7	C₃×#546	C₂	1	4	yes	maximal, complemented
8	C₃×#542	C₂	1	4	yes	maximal, complemented
9	C₃×#538	C₂	1	4	yes	maximal, complemented
10	C₃×#536	C₂	1	2	yes	maximal, complemented
11	C₃×#534	C₂	1	2	yes	maximal, complemented
12	C₃×#529	C₂	1	2	yes	maximal, complemented
13	C₂×C₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
14	#3545	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₃×#41	C₂²	1	2	yes	—
16	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×D₄	C₂²	1	2	yes	complemented
19	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
21	C₃×#126	C₂²	1	4	yes	complemented
22	C₃×#126	C₂²	1	4	yes	complemented
23	C₃×#126	C₂²	1	4	yes	complemented
24	C₃×#125	C₂²	1	2	yes	complemented
25	C₃×#124	C₂²	1	1	yes	characteristic
26	C₃×#124	C₂²	1	1	yes	characteristic
27	C₃×#124	C₂²	1	2	yes	complemented
28	C₃×#124	C₂²	1	2	yes	complemented
29	C₃×#124	C₂²	1	4	yes	complemented
30	C₃×#124	C₂²	1	1	yes	characteristic, complemented
31	C₃×#124	C₂²	1	4	yes	complemented
32	C₃×#124	C₂²	1	1	yes	characteristic, complemented
33	C₃×#124	C₂²	1	2	yes	complemented
34	C₃×#124	C₂²	1	4	yes	complemented
35	C₃×#123	C₂²	1	2	yes	—
36	C₃×#123	C₂²	1	4	yes	complemented
37	C₃×#123	C₂²	1	4	yes	complemented
38	C₃×#123	C₂²	1	4	yes	complemented
39	C₃×#123	C₂²	1	2	yes	complemented
40	C₃×#123	C₂²	1	4	yes	complemented
41	C₃×#123	C₂²	1	4	yes	complemented
42	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
44	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
45	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
46	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
47	C₃×#121	C₂²	1	2	yes	—
48	C₃×#121	C₂²	1	4	yes	—
49	C₃×#121	C₂²	1	4	yes	complemented
50	C₃×#121	C₂²	1	4	yes	complemented
51	C₃×#121	C₂²	1	4	yes	complemented
52	C₃×#120	C₂²	1	2	yes	—
53	C₃×#120	C₂²	1	4	yes	—
54	C₃×#120	C₂²	1	4	yes	complemented
55	C₃×#120	C₂²	1	2	yes	complemented
56	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
57	C₃×C₄×D₄	C₂²	1	2	yes	complemented
58	C₃×C₄×D₄	C₂²	1	4	yes	complemented
59	C₃×C₄×D₄	C₂²	1	4	yes	complemented
60	C₃×C₄×D₄	C₂²	1	4	yes	complemented
61	C₃×#117	C₂²	1	4	yes	complemented
62	C₃×#117	C₂²	1	2	yes	complemented
63	C₃×#117	C₂²	1	4	yes	complemented
64	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
65	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
66	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
67	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
68	#563	C₂×C₃	1	1	yes	characteristic, complemented
69	#562	C₂×C₃	1	2	yes	complemented
70	H(3,𝔽₄)	C₂×C₃	1	1	yes	characteristic, complemented
71	#555	C₂×C₃	1	2	yes	complemented
72	#551	C₂×C₃	1	2	yes	complemented
73	#551	C₂×C₃	1	4	yes	complemented
74	#546	C₂×C₃	1	4	yes	complemented
75	#542	C₂×C₃	1	4	yes	complemented
76	#538	C₂×C₃	1	4	yes	complemented
77	#536	C₂×C₃	1	2	yes	complemented
78	#534	C₂×C₃	1	2	yes	complemented
79	#529	C₂×C₃	1	2	yes	complemented
80	C₂×#124	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂⁴×C₃	C₂³	1	2	yes	—
82	C₂⁴×C₃	C₂³	1	2	yes	—
83	C₃×#41	—	4	4	no	—
84	C₂×C₃×Q₈	—	4	2	no	—
85	C₂×C₃×Q₈	C₂³	1	2	yes	—
86	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
87	C₂×C₃×Q₈	C₂³	1	2	yes	—
88	C₂×C₃×Q₈	C₂³	1	2	yes	—
89	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
90	C₂×C₃×D₄	—	4	2	no	—
91	C₂×C₃×D₄	—	4	4	no	—
92	C₂×C₃×D₄	C₂³	1	4	yes	—
93	C₂×C₃×D₄	C₂³	1	4	yes	—
94	C₂×C₃×D₄	C₂³	1	4	yes	—
95	C₂×C₃×D₄	C₂³	1	2	yes	—
96	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
97	C₂×C₃×D₄	C₂³	1	2	yes	—
98	C₂×C₃×D₄	C₂³	1	2	yes	—
99	C₂×C₃×D₄	C₂³	1	4	yes	—
100	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
101	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₂³	1	2	yes	—
103	C₂²×C₃×C₄	C₂³	1	2	yes	—
104	C₂²×C₃×C₄	C₂³	1	4	yes	—
105	C₂²×C₃×C₄	C₂³	1	4	yes	—
106	C₂²×C₃×C₄	C₂³	1	4	yes	—
107	C₂²×C₃×C₄	C₂³	1	2	yes	—
108	C₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₃×C₄²	C₂³	1	1	yes	characteristic
133	C₃×C₄²	C₂³	1	2	yes	—
134	C₃×C₄²	C₂³	1	1	yes	characteristic
135	C₃×C₄²	C₂³	1	2	yes	—
136	C₃×C₄²	C₂³	1	4	yes	—
137	C₃×C₄²	C₂³	1	2	yes	—
138	C₂×#41	C₂²×C₃	1	2	yes	—
139	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
141	C₂²×D₄	C₂²×C₃	1	2	yes	complemented
142	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
143	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
144	#126	C₂²×C₃	1	4	yes	complemented
145	#126	C₂²×C₃	1	4	yes	complemented
146	#126	C₂²×C₃	1	4	yes	complemented
147	#125	C₂²×C₃	1	2	yes	complemented
148	#124	C₂²×C₃	1	1	yes	characteristic
149	#124	C₂²×C₃	1	1	yes	characteristic
150	#124	C₂²×C₃	1	4	yes	complemented
151	#124	C₂²×C₃	1	1	yes	characteristic, complemented
152	#124	C₂²×C₃	1	1	yes	characteristic, complemented
153	#124	C₂²×C₃	1	2	yes	complemented
154	#124	C₂²×C₃	1	2	yes	complemented
155	#124	C₂²×C₃	1	2	yes	complemented
156	#124	C₂²×C₃	1	4	yes	complemented
157	#124	C₂²×C₃	1	4	yes	complemented
158	#123	C₂²×C₃	1	2	yes	—
159	#123	C₂²×C₃	1	4	yes	complemented
160	#123	C₂²×C₃	1	2	yes	complemented
161	#123	C₂²×C₃	1	4	yes	complemented
162	#123	C₂²×C₃	1	4	yes	complemented
163	#123	C₂²×C₃	1	4	yes	complemented
164	#123	C₂²×C₃	1	4	yes	complemented
165	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
166	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
167	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
168	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
169	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
170	#121	C₂²×C₃	1	2	yes	—
171	#121	C₂²×C₃	1	4	yes	—
172	#121	C₂²×C₃	1	4	yes	complemented
173	#121	C₂²×C₃	1	4	yes	complemented
174	#121	C₂²×C₃	1	4	yes	complemented
175	#120	C₂²×C₃	1	4	yes	—
176	#120	C₂²×C₃	1	2	yes	—
177	#120	C₂²×C₃	1	2	yes	complemented
178	#120	C₂²×C₃	1	4	yes	complemented
179	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
180	C₄×D₄	C₂²×C₃	1	2	yes	complemented
181	C₄×D₄	C₂²×C₃	1	4	yes	complemented
182	C₄×D₄	C₂²×C₃	1	4	yes	complemented
183	C₄×D₄	C₂²×C₃	1	4	yes	complemented
184	#117	C₂²×C₃	1	4	yes	complemented
185	#117	C₂²×C₃	1	2	yes	complemented
186	#117	C₂²×C₃	1	4	yes	complemented
187	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
188	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
189	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
190	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₂³×C₃	—	2	4	no	—
192	C₂³×C₃	—	4	2	no	—
193	C₂³×C₃	—	4	4	no	—
194	C₂³×C₃	—	4	4	no	—
195	C₂³×C₃	C₂⁴	1	2	yes	—
196	C₂³×C₃	C₂⁴	1	4	yes	—
197	C₂³×C₃	C₂⁴	1	2	yes	—
198	C₂³×C₃	C₂⁴	1	1	yes	characteristic
199	C₃×Q₈	—	4	1	no	—
200	C₃×Q₈	—	4	2	no	—
201	C₃×Q₈	—	4	1	no	—
202	C₃×Q₈	—	4	2	no	—
203	C₃×Q₈	—	4	2	no	—
204	C₃×D₄	—	2	8	no	—
205	C₃×D₄	—	4	1	no	—
206	C₃×D₄	—	4	2	no	—
207	C₃×D₄	—	4	1	no	—
208	C₃×D₄	—	4	4	no	—
209	C₃×D₄	—	4	4	no	—
210	C₃×D₄	—	4	4	no	—
211	C₃×D₄	—	4	2	no	—
212	C₃×D₄	—	4	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	4	4	no	—
216	C₂×C₃×C₄	—	4	2	no	—
217	C₂×C₃×C₄	—	4	4	no	—
218	C₂×C₃×C₄	—	4	2	no	—
219	C₂×C₃×C₄	—	4	4	no	—
220	C₂×C₃×C₄	C₂⁴	1	2	yes	—
221	C₂×C₃×C₄	C₂⁴	1	2	yes	—
222	C₂×C₃×C₄	C₂⁴	1	4	yes	—
223	C₂×C₃×C₄	C₂⁴	1	2	yes	—
224	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂⁴	1	4	yes	—
227	C₂×C₃×C₄	C₂⁴	1	4	yes	—
228	C₂×C₃×C₄	C₂⁴	1	2	yes	—
229	C₂⁴	C₂³×C₃	1	2	yes	—
230	C₂⁴	C₂³×C₃	1	2	yes	—
231	#41	—	4	4	no	—
232	C₂×Q₈	—	4	2	no	—
233	C₂×Q₈	C₂³×C₃	1	2	yes	—
234	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
235	C₂×Q₈	C₂³×C₃	1	2	yes	—
236	C₂×Q₈	C₂³×C₃	1	2	yes	—
237	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
238	C₂×D₄	—	4	2	no	—
239	C₂×D₄	—	4	4	no	—
240	C₂×D₄	C₂³×C₃	1	4	yes	—
241	C₂×D₄	C₂³×C₃	1	4	yes	—
242	C₂×D₄	C₂³×C₃	1	4	yes	—
243	C₂×D₄	C₂³×C₃	1	2	yes	—
244	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
245	C₂×D₄	C₂³×C₃	1	2	yes	—
246	C₂×D₄	C₂³×C₃	1	2	yes	—
247	C₂×D₄	C₂³×C₃	1	4	yes	—
248	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
250	C₂²×C₄	C₂³×C₃	1	2	yes	—
251	C₂²×C₄	C₂³×C₃	1	2	yes	—
252	C₂²×C₄	C₂³×C₃	1	4	yes	—
253	C₂²×C₄	C₂³×C₃	1	4	yes	—
254	C₂²×C₄	C₂³×C₃	1	4	yes	—
255	C₂²×C₄	C₂³×C₃	1	2	yes	—
256	C₄⋊C₄	C₂³×C₃	1	4	yes	—
257	C₄⋊C₄	C₂³×C₃	1	4	yes	—
258	C₄⋊C₄	C₂³×C₃	1	4	yes	—
259	C₄⋊C₄	C₂³×C₃	1	4	yes	—
260	C₄⋊C₄	C₂³×C₃	1	4	yes	—
261	C₄⋊C₄	C₂³×C₃	1	4	yes	—
262	C₄⋊C₄	C₂³×C₃	1	2	yes	—
263	C₄⋊C₄	C₂³×C₃	1	2	yes	—
264	C₄⋊C₄	C₂³×C₃	1	4	yes	—
265	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
266	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
267	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
268	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
269	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
270	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
271	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
272	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
273	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
274	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
275	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
276	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
277	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
278	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
279	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
280	C₄²	C₂³×C₃	1	1	yes	characteristic
281	C₄²	C₂³×C₃	1	2	yes	—
282	C₄²	C₂³×C₃	1	1	yes	characteristic
283	C₄²	C₂³×C₃	1	2	yes	—
284	C₄²	C₂³×C₃	1	4	yes	—
285	C₄²	C₂³×C₃	1	2	yes	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	4	no	—
291	C₂²×C₃	—	2	4	no	—
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	4	no	—
294	C₂²×C₃	—	8	4	no	—
295	C₂²×C₃	—	8	4	no	—
296	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
297	C₂²×C₃	C₂⁵	1	1	yes	characteristic
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	2	4	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	4	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	2	4	no	—
307	C₂³	—	2	4	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	4	no	—
310	C₂³	—	4	4	no	—
311	C₂³	C₂⁴×C₃	1	2	yes	—
312	C₂³	C₂⁴×C₃	1	4	yes	—
313	C₂³	C₂⁴×C₃	1	2	yes	—
314	C₂³	C₂⁴×C₃	1	1	yes	characteristic
315	Q₈	—	4	1	no	—
316	Q₈	—	4	2	no	—
317	Q₈	—	4	1	no	—
318	Q₈	—	4	2	no	—
319	Q₈	—	4	2	no	—
320	D₄	—	2	8	no	—
321	D₄	—	4	1	no	—
322	D₄	—	4	2	no	—
323	D₄	—	4	1	no	—
324	D₄	—	4	4	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	4	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₂⁴×C₃	1	2	yes	—
337	C₂×C₄	C₂⁴×C₃	1	2	yes	—
338	C₂×C₄	C₂⁴×C₃	1	4	yes	—
339	C₂×C₄	C₂⁴×C₃	1	2	yes	—
340	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
341	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
342	C₂×C₄	C₂⁴×C₃	1	4	yes	—
343	C₂×C₄	C₂⁴×C₃	1	4	yes	—
344	C₂×C₄	C₂⁴×C₃	1	2	yes	—
345	C₂×C₃	—	2	2	no	—
346	C₂×C₃	—	4	4	no	—
347	C₂×C₃	—	4	2	no	—
348	C₂×C₃	—	4	2	no	—
349	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₃	#585	1	2	yes	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	4	no	—
361	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
362	C₂²	C₂⁵×C₃	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	4	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	4	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	4	no	—
372	C₃	#3545	1	1	yes	characteristic, direct product factor, Sylow
373	C₂	—	2	2	no	—
374	C₂	—	4	2	no	—
375	C₂	—	4	4	no	—
376	C₂	—	4	2	no	—
377	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂	C₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#563	C₂	semidirect
2. C₃×#562	C₂	semidirect
3. C₃×H(3,𝔽₄)	C₂	semidirect
4. C₃×#555	C₂	semidirect
5. C₃×#551	C₂	semidirect
6. C₃×#551	C₂	semidirect
7. C₃×#546	C₂	semidirect
8. C₃×#542	C₂	semidirect
9. C₃×#538	C₂	semidirect
10. C₃×#536	C₂	semidirect
11. C₃×#534	C₂	semidirect
12. C₃×#529	C₂	semidirect
13. C₂×C₃×#124	C₂	semidirect
14. #3545	C₃	direct (N × H)
16. C₂²×C₃×Q₈	C₂²	semidirect
18. C₂²×C₃×D₄	C₂²	semidirect
19. C₃×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₄⋊Q₈	C₂²	semidirect
21. C₃×#126	C₂²	semidirect
22. C₃×#126	C₂²	semidirect
23. C₃×#126	C₂²	semidirect
24. C₃×#125	C₂²	semidirect
27. C₃×#124	C₂²	semidirect
28. C₃×#124	C₂²	semidirect
29. C₃×#124	C₂²	semidirect
30. C₃×#124	C₂²	semidirect
31. C₃×#124	C₂²	semidirect
32. C₃×#124	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
36. C₃×#123	C₂²	semidirect
37. C₃×#123	C₂²	semidirect
38. C₃×#123	C₂²	semidirect
39. C₃×#123	C₂²	semidirect
40. C₃×#123	C₂²	semidirect
41. C₃×#123	C₂²	semidirect
42. C₃×C₂²⋊Q₈	C₂²	semidirect
43. C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₃×C₂²⋊Q₈	C₂²	semidirect
45. C₃×C₂²⋊Q₈	C₂²	semidirect
46. C₃×C₂²⋊Q₈	C₂²	semidirect
49. C₃×#121	C₂²	semidirect
50. C₃×#121	C₂²	semidirect
51. C₃×#121	C₂²	semidirect
54. C₃×#120	C₂²	semidirect
55. C₃×#120	C₂²	semidirect
56. C₃×C₄×Q₈	C₂²	semidirect
57. C₃×C₄×D₄	C₂²	semidirect
58. C₃×C₄×D₄	C₂²	semidirect
59. C₃×C₄×D₄	C₂²	semidirect
60. C₃×C₄×D₄	C₂²	semidirect
61. C₃×#117	C₂²	semidirect
62. C₃×#117	C₂²	semidirect
63. C₃×#117	C₂²	semidirect
64. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
65. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
66. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
67. C₂×C₃×C₄²	C₂²	semidirect
68. #563	C₂×C₃	semidirect
69. #562	C₂×C₃	semidirect
70. H(3,𝔽₄)	C₂×C₃	semidirect
71. #555	C₂×C₃	semidirect
72. #551	C₂×C₃	semidirect
73. #551	C₂×C₃	semidirect
74. #546	C₂×C₃	semidirect
75. #542	C₂×C₃	semidirect
76. #538	C₂×C₃	semidirect
77. #536	C₂×C₃	semidirect
78. #534	C₂×C₃	semidirect
79. #529	C₂×C₃	semidirect
80. C₂×#124	C₂×C₃	semidirect
139. C₂²×Q₈	C₂²×C₃	semidirect
141. C₂²×D₄	C₂²×C₃	semidirect
142. C₄⋊Q₈	C₂²×C₃	semidirect
143. C₄⋊Q₈	C₂²×C₃	semidirect
144. #126	C₂²×C₃	semidirect
145. #126	C₂²×C₃	semidirect
146. #126	C₂²×C₃	semidirect
147. #125	C₂²×C₃	semidirect
150. #124	C₂²×C₃	semidirect
151. #124	C₂²×C₃	semidirect
152. #124	C₂²×C₃	semidirect
153. #124	C₂²×C₃	semidirect
154. #124	C₂²×C₃	semidirect
155. #124	C₂²×C₃	semidirect
156. #124	C₂²×C₃	semidirect
157. #124	C₂²×C₃	semidirect
159. #123	C₂²×C₃	semidirect
160. #123	C₂²×C₃	semidirect
161. #123	C₂²×C₃	semidirect
162. #123	C₂²×C₃	semidirect
163. #123	C₂²×C₃	semidirect
164. #123	C₂²×C₃	semidirect
165. C₂²⋊Q₈	C₂²×C₃	semidirect
166. C₂²⋊Q₈	C₂²×C₃	semidirect
167. C₂²⋊Q₈	C₂²×C₃	semidirect
168. C₂²⋊Q₈	C₂²×C₃	semidirect
169. C₂²⋊Q₈	C₂²×C₃	semidirect
172. #121	C₂²×C₃	semidirect
173. #121	C₂²×C₃	semidirect
174. #121	C₂²×C₃	semidirect
177. #120	C₂²×C₃	semidirect
178. #120	C₂²×C₃	semidirect
179. C₄×Q₈	C₂²×C₃	semidirect
180. C₄×D₄	C₂²×C₃	semidirect
181. C₄×D₄	C₂²×C₃	semidirect
182. C₄×D₄	C₂²×C₃	semidirect
183. C₄×D₄	C₂²×C₃	semidirect
184. #117	C₂²×C₃	semidirect
185. #117	C₂²×C₃	semidirect
186. #117	C₂²×C₃	semidirect
187. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
188. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
189. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
190. C₂×C₄²	C₂²×C₃	semidirect
372. C₃	#3545	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#563	2
C₃×#562	2
C₃×H(3,𝔽₄)	2
C₃×#555	2
C₃×#551	2
C₃×#546	2
C₃×#542	2
C₃×#538	2
C₃×#536	2
C₃×#534	2
C₃×#529	2
C₂×C₃×#124	2
#3545	3

Subgroups — C3×#3545 #87429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3545 #87429