Subgroups — C₃×#3506 #87390

Order 384.

1140 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#559	C₂	1	4	yes	maximal, complemented
2	C₃×#556	C₂	1	2	yes	maximal, complemented
3	C₃×#555	C₂	1	2	yes	maximal, complemented
4	C₃×#553	C₂	1	4	yes	maximal, complemented
5	C₃×#550	C₂	1	2	yes	maximal, complemented
6	C₃×#547	C₂	1	2	yes	maximal, complemented
7	C₃×#538	C₂	1	4	yes	maximal, complemented
8	C₃×#535	C₂	1	2	yes	maximal, complemented
9	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#525	C₂	1	4	yes	maximal, complemented
12	C₃×#520	C₂	1	2	yes	maximal, complemented
13	C₂×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
14	#3506	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₃×#41	C₂²	1	2	yes	—
16	C₂×C₃×#41	C₂²	1	4	yes	complemented
17	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄	C₂²	1	2	yes	—
19	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×#127	C₂²	1	4	yes	—
23	C₃×#127	C₂²	1	1	yes	characteristic, complemented
24	C₃×#126	C₂²	1	8	yes	complemented
25	C₃×#125	C₂²	1	2	yes	complemented
26	C₃×#124	C₂²	1	4	yes	—
27	C₃×#124	C₂²	1	2	yes	complemented
28	C₃×#124	C₂²	1	8	yes	complemented
29	C₃×#123	C₂²	1	8	yes	complemented
30	C₃×#123	C₂²	1	8	yes	complemented
31	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
34	C₃×#121	C₂²	1	2	yes	—
35	C₃×#121	C₂²	1	2	yes	—
36	C₃×#121	C₂²	1	4	yes	—
37	C₃×#121	C₂²	1	4	yes	—
38	C₃×#121	C₂²	1	4	yes	complemented
39	C₃×#121	C₂²	1	8	yes	complemented
40	C₃×#120	C₂²	1	8	yes	—
41	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
42	C₃×C₄×Q₈	C₂²	1	4	yes	complemented
43	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
44	C₃×C₄×D₄	C₂²	1	2	yes	—
45	C₃×C₄×D₄	C₂²	1	2	yes	—
46	C₃×C₄×D₄	C₂²	1	2	yes	—
47	C₃×C₄×D₄	C₂²	1	2	yes	—
48	C₃×C₄×D₄	C₂²	1	8	yes	—
49	C₃×C₄×D₄	C₂²	1	4	yes	complemented
50	C₃×C₄×D₄	C₂²	1	8	yes	complemented
51	C₃×C₄×D₄	C₂²	1	2	yes	complemented
52	C₃×C₄×D₄	C₂²	1	2	yes	complemented
53	C₃×#117	C₂²	1	2	yes	—
54	C₃×#117	C₂²	1	4	yes	complemented
55	C₃×#117	C₂²	1	4	yes	complemented
56	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×C₃×C₄⋊C₄	C₂²	1	4	yes	complemented
58	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
59	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
60	#559	C₂×C₃	1	4	yes	complemented
61	#556	C₂×C₃	1	2	yes	complemented
62	#555	C₂×C₃	1	2	yes	complemented
63	#553	C₂×C₃	1	4	yes	complemented
64	#550	C₂×C₃	1	2	yes	complemented
65	#547	C₂×C₃	1	2	yes	complemented
66	#538	C₂×C₃	1	4	yes	complemented
67	#535	C₂×C₃	1	2	yes	complemented
68	#533	C₂×C₃	1	1	yes	characteristic, complemented
69	#532	C₂×C₃	1	1	yes	characteristic, complemented
70	#525	C₂×C₃	1	4	yes	complemented
71	#520	C₂×C₃	1	2	yes	complemented
72	C₂×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂⁴×C₃	C₂³	1	2	yes	—
74	C₃×#41	—	2	8	no	—
75	C₃×#41	—	4	8	no	—
76	C₂×C₃×Q₈	C₂³	1	2	yes	—
77	C₂×C₃×Q₈	C₂³	1	2	yes	—
78	C₂×C₃×Q₈	C₂³	1	2	yes	—
79	C₂×C₃×D₄	—	2	4	no	—
80	C₂×C₃×D₄	C₂³	1	4	yes	—
81	C₂×C₃×D₄	C₂³	1	2	yes	—
82	C₂×C₃×D₄	C₂³	1	2	yes	—
83	C₂×C₃×D₄	C₂³	1	2	yes	—
84	C₂×C₃×D₄	C₂³	1	2	yes	—
85	C₂×C₃×D₄	C₂³	1	8	yes	—
86	C₂×C₃×D₄	C₂³	1	2	yes	—
87	C₂×C₃×D₄	C₂³	1	8	yes	—
88	C₂²×C₃×C₄	—	4	4	no	—
89	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄	C₂³	1	4	yes	—
91	C₂²×C₃×C₄	C₂³	1	4	yes	—
92	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄	C₂³	1	2	yes	—
94	C₂²×C₃×C₄	C₂³	1	8	yes	—
95	C₂²×C₃×C₄	C₂³	1	4	yes	—
96	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
97	C₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₃×C₄⋊C₄	C₂³	1	8	yes	—
101	C₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
113	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
115	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₃×C₄²	C₂³	1	1	yes	characteristic
117	C₃×C₄²	C₂³	1	1	yes	characteristic
118	C₃×C₄²	C₂³	1	1	yes	characteristic
119	C₃×C₄²	C₂³	1	1	yes	characteristic
120	C₃×C₄²	C₂³	1	4	yes	—
121	C₃×C₄²	C₂³	1	8	yes	—
122	C₂×#41	C₂²×C₃	1	2	yes	—
123	C₂×#41	C₂²×C₃	1	4	yes	complemented
124	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
125	C₂³×C₄	C₂²×C₃	1	2	yes	—
126	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
129	#127	C₂²×C₃	1	4	yes	—
130	#127	C₂²×C₃	1	1	yes	characteristic, complemented
131	#126	C₂²×C₃	1	8	yes	complemented
132	#125	C₂²×C₃	1	2	yes	complemented
133	#124	C₂²×C₃	1	4	yes	—
134	#124	C₂²×C₃	1	2	yes	complemented
135	#124	C₂²×C₃	1	8	yes	complemented
136	#123	C₂²×C₃	1	8	yes	complemented
137	#123	C₂²×C₃	1	8	yes	complemented
138	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
139	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
140	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
141	#121	C₂²×C₃	1	2	yes	—
142	#121	C₂²×C₃	1	2	yes	—
143	#121	C₂²×C₃	1	4	yes	—
144	#121	C₂²×C₃	1	4	yes	—
145	#121	C₂²×C₃	1	4	yes	complemented
146	#121	C₂²×C₃	1	8	yes	complemented
147	#120	C₂²×C₃	1	8	yes	—
148	C₄×Q₈	C₂²×C₃	1	4	yes	complemented
149	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
150	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
151	C₄×D₄	C₂²×C₃	1	2	yes	—
152	C₄×D₄	C₂²×C₃	1	2	yes	—
153	C₄×D₄	C₂²×C₃	1	2	yes	—
154	C₄×D₄	C₂²×C₃	1	2	yes	—
155	C₄×D₄	C₂²×C₃	1	8	yes	—
156	C₄×D₄	C₂²×C₃	1	4	yes	complemented
157	C₄×D₄	C₂²×C₃	1	8	yes	complemented
158	C₄×D₄	C₂²×C₃	1	2	yes	complemented
159	C₄×D₄	C₂²×C₃	1	2	yes	complemented
160	#117	C₂²×C₃	1	2	yes	—
161	#117	C₂²×C₃	1	4	yes	complemented
162	#117	C₂²×C₃	1	4	yes	complemented
163	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
165	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
166	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
167	C₂³×C₃	—	2	4	no	—
168	C₂³×C₃	—	4	2	no	—
169	C₂³×C₃	—	4	2	no	—
170	C₂³×C₃	C₂⁴	1	4	yes	—
171	C₂³×C₃	C₂⁴	1	4	yes	—
172	C₂³×C₃	C₂⁴	1	1	yes	characteristic
173	C₃×Q₈	—	2	4	no	—
174	C₃×Q₈	—	2	4	no	—
175	C₃×Q₈	—	4	2	no	—
176	C₃×D₄	—	2	8	no	—
177	C₃×D₄	—	2	4	no	—
178	C₃×D₄	—	2	4	no	—
179	C₃×D₄	—	2	4	no	—
180	C₃×D₄	—	2	4	no	—
181	C₃×D₄	—	4	2	no	—
182	C₃×D₄	—	4	8	no	—
183	C₃×D₄	—	4	8	no	—
184	C₂×C₃×C₄	—	2	8	no	—
185	C₂×C₃×C₄	—	2	2	no	—
186	C₂×C₃×C₄	—	2	8	no	—
187	C₂×C₃×C₄	—	4	2	no	—
188	C₂×C₃×C₄	—	4	4	no	—
189	C₂×C₃×C₄	—	4	1	no	—
190	C₂×C₃×C₄	—	4	8	no	—
191	C₂×C₃×C₄	#41	1	4	yes	complemented
192	C₂×C₃×C₄	C₂⁴	1	4	yes	—
193	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
194	C₂×C₃×C₄	C₂⁴	1	4	yes	—
195	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
196	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
197	C₂×C₃×C₄	C₂⁴	1	4	yes	—
198	C₂×C₃×C₄	C₂⁴	1	4	yes	—
199	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
200	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
201	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
202	C₂⁴	C₂³×C₃	1	2	yes	—
203	#41	—	2	8	no	—
204	#41	—	4	8	no	—
205	C₂×Q₈	C₂³×C₃	1	2	yes	—
206	C₂×Q₈	C₂³×C₃	1	2	yes	—
207	C₂×Q₈	C₂³×C₃	1	2	yes	—
208	C₂×D₄	—	2	4	no	—
209	C₂×D₄	C₂³×C₃	1	4	yes	—
210	C₂×D₄	C₂³×C₃	1	2	yes	—
211	C₂×D₄	C₂³×C₃	1	2	yes	—
212	C₂×D₄	C₂³×C₃	1	2	yes	—
213	C₂×D₄	C₂³×C₃	1	2	yes	—
214	C₂×D₄	C₂³×C₃	1	8	yes	—
215	C₂×D₄	C₂³×C₃	1	2	yes	—
216	C₂×D₄	C₂³×C₃	1	8	yes	—
217	C₂²×C₄	—	4	4	no	—
218	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₄	C₂³×C₃	1	4	yes	—
220	C₂²×C₄	C₂³×C₃	1	4	yes	—
221	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₄	C₂³×C₃	1	2	yes	—
223	C₂²×C₄	C₂³×C₃	1	8	yes	—
224	C₂²×C₄	C₂³×C₃	1	4	yes	—
225	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
226	C₄⋊C₄	C₂³×C₃	1	2	yes	—
227	C₄⋊C₄	C₂³×C₃	1	2	yes	—
228	C₄⋊C₄	C₂³×C₃	1	2	yes	—
229	C₄⋊C₄	C₂³×C₃	1	8	yes	—
230	C₄⋊C₄	C₂³×C₃	1	2	yes	—
231	C₄⋊C₄	C₂³×C₃	1	2	yes	—
232	C₄⋊C₄	C₂³×C₃	1	2	yes	—
233	C₄⋊C₄	C₂³×C₃	1	4	yes	—
234	C₄⋊C₄	C₂³×C₃	1	2	yes	—
235	C₄⋊C₄	C₂³×C₃	1	4	yes	—
236	C₄⋊C₄	C₂³×C₃	1	2	yes	—
237	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
238	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
239	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
240	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
241	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
242	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
243	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
244	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
245	C₄²	C₂³×C₃	1	1	yes	characteristic
246	C₄²	C₂³×C₃	1	1	yes	characteristic
247	C₄²	C₂³×C₃	1	1	yes	characteristic
248	C₄²	C₂³×C₃	1	1	yes	characteristic
249	C₄²	C₂³×C₃	1	4	yes	—
250	C₄²	C₂³×C₃	1	8	yes	—
251	C₂²×C₃	—	2	1	no	—
252	C₂²×C₃	—	2	1	no	—
253	C₂²×C₃	—	2	4	no	—
254	C₂²×C₃	—	2	4	no	—
255	C₂²×C₃	—	2	4	no	—
256	C₂²×C₃	—	2	4	no	—
257	C₂²×C₃	—	2	4	no	—
258	C₂²×C₃	—	2	4	no	—
259	C₂²×C₃	—	4	8	no	—
260	C₂²×C₃	C₂×#41	1	2	yes	—
261	C₂²×C₃	C₂⁵	1	1	yes	characteristic
262	C₃×C₄	—	2	4	no	—
263	C₃×C₄	—	2	1	no	—
264	C₃×C₄	—	2	4	no	—
265	C₃×C₄	—	2	4	no	—
266	C₃×C₄	—	2	1	no	—
267	C₃×C₄	—	2	1	no	—
268	C₃×C₄	—	2	4	no	—
269	C₃×C₄	C₂×#41	1	2	yes	—
270	C₃×C₄	C₂×#41	1	2	yes	—
271	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
272	C₂³	—	2	4	no	—
273	C₂³	—	4	2	no	—
274	C₂³	—	4	2	no	—
275	C₂³	C₂⁴×C₃	1	4	yes	—
276	C₂³	C₂⁴×C₃	1	4	yes	—
277	C₂³	C₂⁴×C₃	1	1	yes	characteristic
278	Q₈	—	2	4	no	—
279	Q₈	—	2	4	no	—
280	Q₈	—	4	2	no	—
281	D₄	—	2	8	no	—
282	D₄	—	2	4	no	—
283	D₄	—	2	4	no	—
284	D₄	—	2	4	no	—
285	D₄	—	2	4	no	—
286	D₄	—	4	8	no	—
287	D₄	—	4	2	no	—
288	D₄	—	4	8	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	8	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	C₃×#41	1	4	yes	complemented
297	C₂×C₄	C₂⁴×C₃	1	4	yes	—
298	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
299	C₂×C₄	C₂⁴×C₃	1	4	yes	—
300	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
301	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
302	C₂×C₄	C₂⁴×C₃	1	4	yes	—
303	C₂×C₄	C₂⁴×C₃	1	4	yes	—
304	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
305	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
306	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
307	C₂×C₃	—	2	2	no	—
308	C₂×C₃	—	4	4	no	—
309	C₂×C₃	—	4	4	no	—
310	C₂×C₃	C₂²×#41	1	1	yes	characteristic
311	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₃	#585	1	1	yes	characteristic
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	2	4	no	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	4	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	4	8	no	—
322	C₂²	C₂×C₃×#41	1	2	yes	—
323	C₂²	C₂⁵×C₃	1	1	yes	characteristic
324	C₄	—	2	4	no	—
325	C₄	—	2	1	no	—
326	C₄	—	2	4	no	—
327	C₄	—	2	4	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	—	2	4	no	—
331	C₄	C₂×C₃×#41	1	2	yes	—
332	C₄	C₂×C₃×#41	1	2	yes	—
333	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
334	C₃	#3506	1	1	yes	characteristic, direct product factor, Sylow
335	C₂	—	2	2	no	—
336	C₂	—	4	4	no	—
337	C₂	—	4	4	no	—
338	C₂	C₂²×C₃×#41	1	1	yes	characteristic
339	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
340	C₂	C₃×#585	1	1	yes	characteristic

	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×#559	C₂	semidirect
2. C₃×#556	C₂	semidirect
3. C₃×#555	C₂	semidirect
4. C₃×#553	C₂	semidirect
5. C₃×#550	C₂	semidirect
6. C₃×#547	C₂	semidirect
7. C₃×#538	C₂	semidirect
8. C₃×#535	C₂	semidirect
9. C₃×#533	C₂	semidirect
10. C₃×#532	C₂	semidirect
11. C₃×#525	C₂	semidirect
12. C₃×#520	C₂	semidirect
13. C₂×C₃×C₄×D₄	C₂	semidirect
14. #3506	C₃	direct (N × H)
16. C₂×C₃×#41	C₂²	semidirect
19. C₃×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₄⋊Q₈	C₂²	semidirect
21. C₃×C₄⋊Q₈	C₂²	semidirect
23. C₃×#127	C₂²	semidirect
24. C₃×#126	C₂²	semidirect
25. C₃×#125	C₂²	semidirect
27. C₃×#124	C₂²	semidirect
28. C₃×#124	C₂²	semidirect
29. C₃×#123	C₂²	semidirect
30. C₃×#123	C₂²	semidirect
33. C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₃×#121	C₂²	semidirect
39. C₃×#121	C₂²	semidirect
41. C₃×C₄×Q₈	C₂²	semidirect
42. C₃×C₄×Q₈	C₂²	semidirect
43. C₃×C₄×Q₈	C₂²	semidirect
49. C₃×C₄×D₄	C₂²	semidirect
50. C₃×C₄×D₄	C₂²	semidirect
51. C₃×C₄×D₄	C₂²	semidirect
52. C₃×C₄×D₄	C₂²	semidirect
54. C₃×#117	C₂²	semidirect
55. C₃×#117	C₂²	semidirect
57. C₂×C₃×C₄⋊C₄	C₂²	semidirect
60. #559	C₂×C₃	semidirect
61. #556	C₂×C₃	semidirect
62. #555	C₂×C₃	semidirect
63. #553	C₂×C₃	semidirect
64. #550	C₂×C₃	semidirect
65. #547	C₂×C₃	semidirect
66. #538	C₂×C₃	semidirect
67. #535	C₂×C₃	semidirect
68. #533	C₂×C₃	semidirect
69. #532	C₂×C₃	semidirect
70. #525	C₂×C₃	semidirect
71. #520	C₂×C₃	semidirect
72. C₂×C₄×D₄	C₂×C₃	semidirect
123. C₂×#41	C₂²×C₃	semidirect
126. C₄⋊Q₈	C₂²×C₃	semidirect
127. C₄⋊Q₈	C₂²×C₃	semidirect
128. C₄⋊Q₈	C₂²×C₃	semidirect
130. #127	C₂²×C₃	semidirect
131. #126	C₂²×C₃	semidirect
132. #125	C₂²×C₃	semidirect
134. #124	C₂²×C₃	semidirect
135. #124	C₂²×C₃	semidirect
136. #123	C₂²×C₃	semidirect
137. #123	C₂²×C₃	semidirect
140. C₂²⋊Q₈	C₂²×C₃	semidirect
145. #121	C₂²×C₃	semidirect
146. #121	C₂²×C₃	semidirect
148. C₄×Q₈	C₂²×C₃	semidirect
149. C₄×Q₈	C₂²×C₃	semidirect
150. C₄×Q₈	C₂²×C₃	semidirect
156. C₄×D₄	C₂²×C₃	semidirect
157. C₄×D₄	C₂²×C₃	semidirect
158. C₄×D₄	C₂²×C₃	semidirect
159. C₄×D₄	C₂²×C₃	semidirect
161. #117	C₂²×C₃	semidirect
162. #117	C₂²×C₃	semidirect
164. C₂×C₄⋊C₄	C₂²×C₃	semidirect
191. C₂×C₃×C₄	#41	semidirect
296. C₂×C₄	C₃×#41	semidirect
334. C₃	#3506	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×#559	2
C₃×#556	2
C₃×#555	2
C₃×#553	2
C₃×#550	2
C₃×#547	2
C₃×#538	2
C₃×#535	2
C₃×#533	2
C₃×#532	2
C₃×#525	2
C₃×#520	2
C₂×C₃×C₄×D₄	2
#3506	3

Subgroups — C3×#3506 #87390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3506 #87390