Subgroups — C₃×#3539 #87423

Order 384.

1050 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×#560	C₂	1	4	yes	maximal, complemented
2	C₃×#553	C₂	1	2	yes	maximal, complemented
3	C₃×#553	C₂	1	4	yes	maximal, complemented
4	C₃×#552	C₂	1	2	yes	maximal, complemented
5	C₃×#550	C₂	1	2	yes	maximal, complemented
6	C₃×#547	C₂	1	2	yes	maximal, complemented
7	C₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#540	C₂	1	4	yes	maximal, complemented
10	C₃×#539	C₂	1	4	yes	maximal, complemented
11	C₃×#537	C₂	1	2	yes	maximal, complemented
12	C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#525	C₂	1	2	yes	maximal, complemented
14	#3539	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₃×#41	C₂²	1	1	yes	characteristic
16	C₂×C₃×#41	C₂²	1	2	yes	—
17	C₂×C₃×#41	C₂²	1	2	yes	complemented
18	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
19	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×#127	C₂²	1	4	yes	—
21	C₃×#127	C₂²	1	1	yes	characteristic, complemented
22	C₃×#126	C₂²	1	4	yes	—
23	C₃×#126	C₂²	1	4	yes	—
24	C₃×#126	C₂²	1	4	yes	complemented
25	C₃×#125	C₂²	1	4	yes	complemented
26	C₃×#125	C₂²	1	4	yes	complemented
27	C₃×#125	C₂²	1	1	yes	characteristic, complemented
28	C₃×#125	C₂²	1	1	yes	characteristic, complemented
29	C₃×#123	C₂²	1	4	yes	—
30	C₃×#123	C₂²	1	4	yes	—
31	C₃×#123	C₂²	1	4	yes	—
32	C₃×#123	C₂²	1	4	yes	—
33	C₃×#123	C₂²	1	2	yes	—
34	C₃×#123	C₂²	1	4	yes	complemented
35	C₃×#123	C₂²	1	4	yes	complemented
36	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
40	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₃×#121	C₂²	1	4	yes	—
42	C₃×#121	C₂²	1	4	yes	—
43	C₃×#121	C₂²	1	4	yes	—
44	C₃×#121	C₂²	1	4	yes	—
45	C₃×#121	C₂²	1	4	yes	—
46	C₃×#121	C₂²	1	4	yes	—
47	C₃×#121	C₂²	1	2	yes	—
48	C₃×#121	C₂²	1	2	yes	—
49	C₃×#121	C₂²	1	2	yes	—
50	C₃×#121	C₂²	1	4	yes	complemented
51	C₃×#121	C₂²	1	2	yes	complemented
52	C₃×#121	C₂²	1	4	yes	complemented
53	C₃×#120	C₂²	1	2	yes	—
54	C₃×#120	C₂²	1	4	yes	—
55	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
56	C₃×C₄×D₄	C₂²	1	4	yes	—
57	C₃×C₄×D₄	C₂²	1	2	yes	—
58	C₃×C₄×D₄	C₂²	1	2	yes	—
59	C₃×C₄×D₄	C₂²	1	4	yes	—
60	C₃×C₄×D₄	C₂²	1	4	yes	complemented
61	C₃×C₄×D₄	C₂²	1	2	yes	complemented
62	C₃×C₄×D₄	C₂²	1	4	yes	complemented
63	C₃×#117	C₂²	1	1	yes	characteristic
64	C₃×#117	C₂²	1	2	yes	—
65	C₃×#117	C₂²	1	4	yes	complemented
66	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
67	C₂×C₃×C₄⋊C₄	C₂²	1	4	yes	complemented
68	#560	C₂×C₃	1	4	yes	complemented
69	#553	C₂×C₃	1	2	yes	complemented
70	#553	C₂×C₃	1	4	yes	complemented
71	#552	C₂×C₃	1	2	yes	complemented
72	#550	C₂×C₃	1	2	yes	complemented
73	#547	C₂×C₃	1	2	yes	complemented
74	#541	C₂×C₃	1	1	yes	characteristic, complemented
75	#540	C₂×C₃	1	1	yes	characteristic, complemented
76	#540	C₂×C₃	1	4	yes	complemented
77	#539	C₂×C₃	1	4	yes	complemented
78	#537	C₂×C₃	1	2	yes	complemented
79	#525	C₂×C₃	1	1	yes	characteristic, complemented
80	#525	C₂×C₃	1	2	yes	complemented
81	C₂⁴×C₃	C₂³	1	1	yes	characteristic
82	C₃×#41	—	4	2	no	—
83	C₃×#41	—	4	4	no	—
84	C₃×#41	—	4	4	no	—
85	C₂×C₃×Q₈	C₂³	1	2	yes	—
86	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
87	C₂×C₃×D₄	C₂³	1	2	yes	—
88	C₂×C₃×D₄	C₂³	1	2	yes	—
89	C₂×C₃×D₄	C₂³	1	4	yes	—
90	C₂×C₃×D₄	C₂³	1	4	yes	—
91	C₂×C₃×D₄	C₂³	1	2	yes	—
92	C₂×C₃×D₄	C₂³	1	4	yes	—
93	C₂×C₃×D₄	C₂³	1	4	yes	—
94	C₂×C₃×D₄	C₂³	1	2	yes	—
95	C₂×C₃×D₄	C₂³	1	4	yes	—
96	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
97	C₂×C₃×D₄	C₂³	1	4	yes	—
98	C₂²×C₃×C₄	—	4	2	no	—
99	C₂²×C₃×C₄	C₂³	1	2	yes	—
100	C₂²×C₃×C₄	C₂³	1	2	yes	—
101	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₂³	1	4	yes	—
103	C₂²×C₃×C₄	C₂³	1	4	yes	—
104	C₂²×C₃×C₄	C₂³	1	4	yes	—
105	C₂²×C₃×C₄	C₂³	1	4	yes	—
106	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₄	C₂³	1	2	yes	—
108	C₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₃×C₄⋊C₄	C₂³	1	2	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	4	yes	—
115	C₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₃×C₄²	C₂³	1	4	yes	—
135	C₃×C₄²	C₂³	1	1	yes	characteristic
136	C₃×C₄²	C₂³	1	1	yes	characteristic
137	C₃×C₄²	C₂³	1	4	yes	—
138	C₂×#41	C₂²×C₃	1	1	yes	characteristic
139	C₂×#41	C₂²×C₃	1	2	yes	—
140	C₂×#41	C₂²×C₃	1	2	yes	complemented
141	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
142	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
143	#127	C₂²×C₃	1	4	yes	—
144	#127	C₂²×C₃	1	1	yes	characteristic, complemented
145	#126	C₂²×C₃	1	4	yes	—
146	#126	C₂²×C₃	1	4	yes	—
147	#126	C₂²×C₃	1	4	yes	complemented
148	#125	C₂²×C₃	1	4	yes	complemented
149	#125	C₂²×C₃	1	4	yes	complemented
150	#125	C₂²×C₃	1	1	yes	characteristic, complemented
151	#125	C₂²×C₃	1	1	yes	characteristic, complemented
152	#123	C₂²×C₃	1	4	yes	—
153	#123	C₂²×C₃	1	2	yes	—
154	#123	C₂²×C₃	1	4	yes	—
155	#123	C₂²×C₃	1	4	yes	—
156	#123	C₂²×C₃	1	4	yes	—
157	#123	C₂²×C₃	1	4	yes	complemented
158	#123	C₂²×C₃	1	4	yes	complemented
159	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
160	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
161	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
162	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
163	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
164	#121	C₂²×C₃	1	2	yes	—
165	#121	C₂²×C₃	1	2	yes	—
166	#121	C₂²×C₃	1	2	yes	—
167	#121	C₂²×C₃	1	4	yes	—
168	#121	C₂²×C₃	1	4	yes	—
169	#121	C₂²×C₃	1	4	yes	—
170	#121	C₂²×C₃	1	4	yes	—
171	#121	C₂²×C₃	1	4	yes	—
172	#121	C₂²×C₃	1	4	yes	—
173	#121	C₂²×C₃	1	4	yes	complemented
174	#121	C₂²×C₃	1	2	yes	complemented
175	#121	C₂²×C₃	1	4	yes	complemented
176	#120	C₂²×C₃	1	2	yes	—
177	#120	C₂²×C₃	1	4	yes	—
178	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
179	C₄×D₄	C₂²×C₃	1	4	yes	—
180	C₄×D₄	C₂²×C₃	1	2	yes	—
181	C₄×D₄	C₂²×C₃	1	2	yes	—
182	C₄×D₄	C₂²×C₃	1	4	yes	—
183	C₄×D₄	C₂²×C₃	1	4	yes	complemented
184	C₄×D₄	C₂²×C₃	1	2	yes	complemented
185	C₄×D₄	C₂²×C₃	1	4	yes	complemented
186	#117	C₂²×C₃	1	1	yes	characteristic
187	#117	C₂²×C₃	1	2	yes	—
188	#117	C₂²×C₃	1	4	yes	complemented
189	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
190	C₂×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
191	C₂³×C₃	—	4	1	no	—
192	C₂³×C₃	—	4	2	no	—
193	C₂³×C₃	C₂⁴	1	1	yes	characteristic
194	C₂³×C₃	C₂⁴	1	2	yes	—
195	C₂³×C₃	C₂⁴	1	2	yes	—
196	C₂³×C₃	C₂⁴	1	4	yes	—
197	C₃×Q₈	—	2	4	no	—
198	C₃×Q₈	—	4	1	no	—
199	C₃×D₄	—	2	4	no	—
200	C₃×D₄	—	4	2	no	—
201	C₃×D₄	—	4	4	no	—
202	C₃×D₄	—	4	4	no	—
203	C₃×D₄	—	4	4	no	—
204	C₃×D₄	—	4	2	no	—
205	C₃×D₄	—	4	4	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	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	4	1	no	—
214	C₂×C₃×C₄	—	4	2	no	—
215	C₂×C₃×C₄	—	4	4	no	—
216	C₂×C₃×C₄	—	4	4	no	—
217	C₂×C₃×C₄	—	4	4	no	—
218	C₂×C₃×C₄	—	4	4	no	—
219	C₂×C₃×C₄	C₂⁴	1	2	yes	—
220	C₂×C₃×C₄	C₂⁴	1	4	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	4	yes	—
225	C₂×C₃×C₄	C₂⁴	1	2	yes	—
226	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
228	C₂⁴	C₂³×C₃	1	1	yes	characteristic
229	#41	—	4	2	no	—
230	#41	—	4	4	no	—
231	#41	—	4	4	no	—
232	C₂×Q₈	C₂³×C₃	1	2	yes	—
233	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
234	C₂×D₄	C₂³×C₃	1	2	yes	—
235	C₂×D₄	C₂³×C₃	1	2	yes	—
236	C₂×D₄	C₂³×C₃	1	4	yes	—
237	C₂×D₄	C₂³×C₃	1	4	yes	—
238	C₂×D₄	C₂³×C₃	1	2	yes	—
239	C₂×D₄	C₂³×C₃	1	4	yes	—
240	C₂×D₄	C₂³×C₃	1	4	yes	—
241	C₂×D₄	C₂³×C₃	1	2	yes	—
242	C₂×D₄	C₂³×C₃	1	4	yes	—
243	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
244	C₂×D₄	C₂³×C₃	1	4	yes	—
245	C₂²×C₄	—	4	2	no	—
246	C₂²×C₄	C₂³×C₃	1	2	yes	—
247	C₂²×C₄	C₂³×C₃	1	2	yes	—
248	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₃	1	4	yes	—
250	C₂²×C₄	C₂³×C₃	1	4	yes	—
251	C₂²×C₄	C₂³×C₃	1	4	yes	—
252	C₂²×C₄	C₂³×C₃	1	4	yes	—
253	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₄	C₂³×C₃	1	2	yes	—
255	C₄⋊C₄	C₂³×C₃	1	2	yes	—
256	C₄⋊C₄	C₂³×C₃	1	2	yes	—
257	C₄⋊C₄	C₂³×C₃	1	2	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	4	yes	—
264	C₄⋊C₄	C₂³×C₃	1	2	yes	—
265	C₄⋊C₄	C₂³×C₃	1	4	yes	—
266	C₄⋊C₄	C₂³×C₃	1	4	yes	—
267	C₄⋊C₄	C₂³×C₃	1	4	yes	—
268	C₂²⋊C₄	C₂³×C₃	1	2	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	4	yes	—
273	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
274	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
275	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
276	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
277	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
278	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
279	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
280	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
281	C₄²	C₂³×C₃	1	4	yes	—
282	C₄²	C₂³×C₃	1	1	yes	characteristic
283	C₄²	C₂³×C₃	1	1	yes	characteristic
284	C₄²	C₂³×C₃	1	4	yes	—
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	4	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	4	no	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	4	4	no	—
297	C₂²×C₃	C₂⁵	1	1	yes	characteristic
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	2	no	—
301	C₃×C₄	—	2	4	no	—
302	C₃×C₄	—	2	2	no	—
303	C₃×C₄	—	2	4	no	—
304	C₃×C₄	—	2	4	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	2	no	—
309	C₂³	C₂⁴×C₃	1	1	yes	characteristic
310	C₂³	C₂⁴×C₃	1	2	yes	—
311	C₂³	C₂⁴×C₃	1	2	yes	—
312	C₂³	C₂⁴×C₃	1	4	yes	—
313	Q₈	—	2	4	no	—
314	Q₈	—	4	1	no	—
315	D₄	—	2	4	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	1	no	—
318	D₄	—	4	4	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	4	no	—
322	D₄	—	4	4	no	—
323	D₄	—	4	4	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	C₂⁴×C₃	1	2	yes	—
336	C₂×C₄	C₂⁴×C₃	1	4	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	4	yes	—
341	C₂×C₄	C₂⁴×C₃	1	2	yes	—
342	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
343	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
344	C₂×C₃	—	4	2	no	—
345	C₂×C₃	—	4	4	no	—
346	C₂×C₃	—	4	2	no	—
347	C₂×C₃	—	4	1	no	—
348	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₃	#585	1	2	yes	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	4	4	no	—
362	C₂²	C₂⁵×C₃	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	4	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	4	no	—
369	C₄	—	2	4	no	—
370	C₄	—	2	2	no	—
371	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
372	C₃	#3539	1	1	yes	characteristic, direct product factor, Sylow
373	C₂	—	4	2	no	—
374	C₂	—	4	1	no	—
375	C₂	—	4	2	no	—
376	C₂	—	4	4	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×#560	C₂	semidirect
2. C₃×#553	C₂	semidirect
3. C₃×#553	C₂	semidirect
4. C₃×#552	C₂	semidirect
5. C₃×#550	C₂	semidirect
6. C₃×#547	C₂	semidirect
7. C₃×#541	C₂	semidirect
8. C₃×#540	C₂	semidirect
9. C₃×#540	C₂	semidirect
10. C₃×#539	C₂	semidirect
11. C₃×#537	C₂	semidirect
12. C₃×#525	C₂	semidirect
13. C₃×#525	C₂	semidirect
14. #3539	C₃	direct (N × H)
17. C₂×C₃×#41	C₂²	semidirect
19. C₃×C₄⋊Q₈	C₂²	semidirect
21. C₃×#127	C₂²	semidirect
24. C₃×#126	C₂²	semidirect
25. C₃×#125	C₂²	semidirect
26. C₃×#125	C₂²	semidirect
27. C₃×#125	C₂²	semidirect
28. C₃×#125	C₂²	semidirect
34. C₃×#123	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
39. C₃×C₂²⋊Q₈	C₂²	semidirect
40. C₃×C₂²⋊Q₈	C₂²	semidirect
50. C₃×#121	C₂²	semidirect
51. C₃×#121	C₂²	semidirect
52. C₃×#121	C₂²	semidirect
55. C₃×C₄×Q₈	C₂²	semidirect
60. C₃×C₄×D₄	C₂²	semidirect
61. C₃×C₄×D₄	C₂²	semidirect
62. C₃×C₄×D₄	C₂²	semidirect
65. C₃×#117	C₂²	semidirect
66. C₂×C₃×C₄⋊C₄	C₂²	semidirect
67. C₂×C₃×C₄⋊C₄	C₂²	semidirect
68. #560	C₂×C₃	semidirect
69. #553	C₂×C₃	semidirect
70. #553	C₂×C₃	semidirect
71. #552	C₂×C₃	semidirect
72. #550	C₂×C₃	semidirect
73. #547	C₂×C₃	semidirect
74. #541	C₂×C₃	semidirect
75. #540	C₂×C₃	semidirect
76. #540	C₂×C₃	semidirect
77. #539	C₂×C₃	semidirect
78. #537	C₂×C₃	semidirect
79. #525	C₂×C₃	semidirect
80. #525	C₂×C₃	semidirect
140. C₂×#41	C₂²×C₃	semidirect
142. C₄⋊Q₈	C₂²×C₃	semidirect
144. #127	C₂²×C₃	semidirect
147. #126	C₂²×C₃	semidirect
148. #125	C₂²×C₃	semidirect
149. #125	C₂²×C₃	semidirect
150. #125	C₂²×C₃	semidirect
151. #125	C₂²×C₃	semidirect
157. #123	C₂²×C₃	semidirect
158. #123	C₂²×C₃	semidirect
162. C₂²⋊Q₈	C₂²×C₃	semidirect
163. C₂²⋊Q₈	C₂²×C₃	semidirect
173. #121	C₂²×C₃	semidirect
174. #121	C₂²×C₃	semidirect
175. #121	C₂²×C₃	semidirect
178. C₄×Q₈	C₂²×C₃	semidirect
183. C₄×D₄	C₂²×C₃	semidirect
184. C₄×D₄	C₂²×C₃	semidirect
185. C₄×D₄	C₂²×C₃	semidirect
188. #117	C₂²×C₃	semidirect
189. C₂×C₄⋊C₄	C₂²×C₃	semidirect
190. C₂×C₄⋊C₄	C₂²×C₃	semidirect
372. C₃	#3539	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×#560	2
C₃×#553	2
C₃×#552	2
C₃×#550	2
C₃×#547	2
C₃×#541	2
C₃×#540	2
C₃×#539	2
C₃×#537	2
C₃×#525	2
#3539	3

Subgroups — C3×#3539 #87423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3539 #87423