Subgroups — C₃×#60490 #10679097

Order 768.

2178 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#518	C₂	1	1	yes	maximal, characteristic
3	C₃×#3081	C₂	1	16	yes	maximal, complemented
4	C₃×#3077	C₂	1	8	yes	maximal, complemented
5	C₃×#2911	C₂	1	2	yes	maximal, complemented
6	C₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#418	C₂	1	2	yes	maximal
8	#60490	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
11	C₃×#544	—	2	2	no	—
12	C₃×#544	C₂²	1	8	yes	complemented
13	C₃×#543	—	2	2	no	—
14	C₃×#533	—	2	4	no	—
15	C₃×#533	C₂²	1	4	yes	complemented
16	C₃×#518	—	2	4	no	—
17	C₃×#518	C₂²	1	8	yes	—
18	C₂×C₃×C₄×D₄	—	2	2	no	—
19	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
20	C₂×C₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₃×#117	C₂²	1	2	yes	—
22	C₂×C₃×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₂²⋊C₄	—	2	2	no	—
24	C₃×#478	C₂²	1	32	yes	complemented
25	C₃×#476	C₂²	1	16	yes	complemented
26	C₃×#474	C₂²	1	16	yes	complemented
27	C₃×#428	C₂²	1	8	yes	complemented
28	C₃×#428	C₂²	1	8	yes	complemented
29	C₃×#427	C₂²	1	8	yes	complemented
30	C₃×#424	C₂²	1	8	yes	complemented
31	C₃×#423	C₂²	1	4	yes	complemented
32	C₃×#418	C₂²	1	8	yes	—
33	C₃×#418	C₂²	1	8	yes	—
34	C₂×C₃×#102	C₂²	1	8	yes	—
35	#3458	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#518	C₂×C₃	1	1	yes	characteristic
37	#3081	C₂×C₃	1	16	yes	complemented
38	#3077	C₂×C₃	1	8	yes	complemented
39	#2911	C₂×C₃	1	2	yes	complemented
40	#2905	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×#418	C₂×C₃	1	2	yes	—
42	C₂⁵×C₃	—	2	1	no	—
43	C₂²×C₃×D₄	—	2	1	no	—
44	C₂²×C₃×D₄	—	2	2	no	—
45	C₂²×C₃×D₄	—	2	4	no	—
46	C₂²×C₃×D₄	Q₈	1	8	yes	complemented
47	C₂²×C₃×D₄	C₂³	1	4	yes	—
48	C₂²×C₃×D₄	C₂³	1	2	yes	—
49	C₂³×C₃×C₄	—	2	4	no	—
50	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃×M₁₆	—	2	8	no	—
52	C₂×C₃×M₁₆	C₂³	1	4	yes	—
53	C₂×C₃×M₁₆	C₂³	1	4	yes	—
54	C₂²×C₃×C₈	C₂³	1	4	yes	—
55	C₃×C₄⋊Q₈	—	2	8	no	—
56	C₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
57	C₃×#125	—	2	8	no	—
58	C₃×#125	C₂³	1	8	yes	complemented
59	C₃×C₂²⋊Q₈	—	2	8	no	—
60	C₃×C₂²⋊Q₈	—	2	16	no	—
61	C₃×C₄×Q₈	—	2	8	no	—
62	C₃×C₄×D₄	—	2	16	no	—
63	C₃×C₄×D₄	—	2	8	no	—
64	C₃×C₄×D₄	C₂³	1	16	yes	—
65	C₃×#117	—	2	2	no	—
66	C₃×#117	—	2	2	no	—
67	C₃×#117	—	2	2	no	—
68	C₃×#117	D₄	1	4	yes	—
69	C₃×#117	C₂³	1	4	yes	—
70	C₃×#117	C₂³	1	4	yes	—
71	C₃×#117	C₂³	1	4	yes	—
72	C₃×#117	C₂³	1	4	yes	—
73	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
74	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
79	C₂×C₃×C₂²⋊C₄	—	2	16	no	—
80	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
81	C₂×C₃×C₄²	—	2	1	no	—
82	C₂×C₃×C₄²	—	2	2	no	—
83	C₂×C₃×C₄²	C₂³	1	2	yes	—
84	C₃×#107	C₂³	1	16	yes	complemented
85	C₃×#106	C₂³	1	16	yes	complemented
86	C₃×C₄⋊C₈	C₂³	1	16	yes	complemented
87	C₃×#102	C₂³	1	32	yes	—
88	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
89	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
90	#544	—	2	2	no	—
91	#544	C₂²×C₃	1	8	yes	complemented
92	#543	—	2	2	no	—
93	#533	—	2	4	no	—
94	#533	C₂²×C₃	1	4	yes	complemented
95	#518	—	2	4	no	—
96	#518	C₂²×C₃	1	8	yes	—
97	C₂×C₄×D₄	—	2	2	no	—
98	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
99	C₂×#117	C₂²×C₃	1	2	yes	—
100	C₂×#117	C₂²×C₃	1	1	yes	characteristic
101	C₂×#117	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₂²⋊C₄	—	2	2	no	—
103	#478	C₂²×C₃	1	32	yes	complemented
104	#476	C₂²×C₃	1	16	yes	complemented
105	#474	C₂²×C₃	1	16	yes	complemented
106	#428	C₂²×C₃	1	8	yes	complemented
107	#428	C₂²×C₃	1	8	yes	complemented
108	#427	C₂²×C₃	1	8	yes	complemented
109	#424	C₂²×C₃	1	8	yes	complemented
110	#423	C₂²×C₃	1	4	yes	complemented
111	#418	C₂²×C₃	1	8	yes	—
112	#418	C₂²×C₃	1	8	yes	—
113	C₂×#102	C₂²×C₃	1	8	yes	—
114	C₂⁴×C₃	—	2	2	no	—
115	C₂⁴×C₃	—	2	8	no	—
116	C₂⁴×C₃	—	2	4	no	—
117	C₂⁴×C₃	—	8	4	no	—
118	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×Q₈	—	2	8	no	—
120	C₂×C₃×D₄	—	2	8	no	—
121	C₂×C₃×D₄	—	2	16	no	—
122	C₂×C₃×D₄	—	2	2	no	—
123	C₂×C₃×D₄	—	2	4	no	—
124	C₂×C₃×D₄	—	2	8	no	—
125	C₂×C₃×D₄	—	2	4	no	—
126	C₂×C₃×D₄	C₂×Q₈	1	8	yes	—
127	C₂×C₃×D₄	C₂×Q₈	1	16	yes	—
128	C₂×C₃×D₄	C₂⁴	1	4	yes	—
129	C₂²×C₃×C₄	—	2	2	no	—
130	C₂²×C₃×C₄	—	2	4	no	—
131	C₂²×C₃×C₄	—	2	16	no	—
132	C₂²×C₃×C₄	—	8	8	no	—
133	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
134	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
136	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
137	C₂²×C₃×C₄	#41	1	4	yes	—
138	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
140	C₃×M₁₆	—	2	8	no	—
141	C₃×M₁₆	—	2	8	no	—
142	C₂×C₃×C₈	—	2	8	no	—
143	C₂×C₃×C₈	C₂⁴	1	8	yes	—
144	C₃×C₄⋊C₄	—	2	2	no	—
145	C₃×C₄⋊C₄	—	2	4	no	—
146	C₃×C₄⋊C₄	—	2	8	no	—
147	C₃×C₄⋊C₄	—	2	16	no	—
148	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
149	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
150	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
151	C₃×C₂²⋊C₄	—	2	4	no	—
152	C₃×C₂²⋊C₄	—	2	4	no	—
153	C₃×C₂²⋊C₄	—	2	4	no	—
154	C₃×C₂²⋊C₄	—	2	16	no	—
155	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
156	C₃×C₄²	—	2	4	no	—
157	C₃×C₄²	—	2	4	no	—
158	C₃×C₄²	—	2	4	no	—
159	C₃×C₄²	C₂×D₄	1	4	yes	—
160	C₃×C₄²	C₂⁴	1	4	yes	—
161	C₂⁵	—	2	1	no	—
162	C₂²×D₄	—	2	1	no	—
163	C₂²×D₄	—	2	2	no	—
164	C₂²×D₄	—	2	4	no	—
165	C₂²×D₄	C₃×Q₈	1	8	yes	complemented
166	C₂²×D₄	C₂³×C₃	1	2	yes	—
167	C₂²×D₄	C₂³×C₃	1	4	yes	—
168	C₂³×C₄	—	2	4	no	—
169	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
170	C₂×M₁₆	—	2	8	no	—
171	C₂×M₁₆	C₂³×C₃	1	4	yes	—
172	C₂×M₁₆	C₂³×C₃	1	4	yes	—
173	C₂²×C₈	C₂³×C₃	1	4	yes	—
174	C₄⋊Q₈	—	2	8	no	—
175	C₄⋊Q₈	C₂³×C₃	1	8	yes	complemented
176	#125	—	2	8	no	—
177	#125	C₂³×C₃	1	8	yes	complemented
178	C₂²⋊Q₈	—	2	8	no	—
179	C₂²⋊Q₈	—	2	16	no	—
180	C₄×Q₈	—	2	8	no	—
181	C₄×D₄	—	2	16	no	—
182	C₄×D₄	—	2	8	no	—
183	C₄×D₄	C₂³×C₃	1	16	yes	—
184	#117	—	2	2	no	—
185	#117	—	2	2	no	—
186	#117	—	2	2	no	—
187	#117	C₃×D₄	1	4	yes	—
188	#117	C₂³×C₃	1	4	yes	—
189	#117	C₂³×C₃	1	4	yes	—
190	#117	C₂³×C₃	1	4	yes	—
191	#117	C₂³×C₃	1	4	yes	—
192	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
193	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
194	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
195	C₂×C₂²⋊C₄	—	2	1	no	—
196	C₂×C₂²⋊C₄	—	2	2	no	—
197	C₂×C₂²⋊C₄	—	2	4	no	—
198	C₂×C₂²⋊C₄	—	2	16	no	—
199	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
200	C₂×C₄²	—	2	1	no	—
201	C₂×C₄²	—	2	2	no	—
202	C₂×C₄²	C₂³×C₃	1	2	yes	—
203	#107	C₂³×C₃	1	16	yes	complemented
204	#106	C₂³×C₃	1	16	yes	complemented
205	C₄⋊C₈	C₂³×C₃	1	16	yes	complemented
206	#102	C₂³×C₃	1	32	yes	—
207	C₂³×C₃	—	2	8	no	—
208	C₂³×C₃	—	2	4	no	—
209	C₂³×C₃	—	2	16	no	—
210	C₂³×C₃	—	4	2	no	—
211	C₂³×C₃	—	4	8	no	—
212	C₂³×C₃	—	8	8	no	—
213	C₂³×C₃	—	8	16	no	—
214	C₂³×C₃	C₂²⋊Q₈	1	4	yes	—
215	C₂³×C₃	C₂²×D₄	1	2	yes	—
216	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
217	C₃×Q₈	—	8	8	no	—
218	C₃×D₄	—	2	8	no	—
219	C₃×D₄	—	2	16	no	—
220	C₃×D₄	—	2	4	no	—
221	C₃×D₄	C₂²×Q₈	1	8	yes	—
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	2	8	no	—
224	C₂×C₃×C₄	—	4	4	no	—
225	C₂×C₃×C₄	—	4	4	no	—
226	C₂×C₃×C₄	—	8	16	no	—
227	C₂×C₃×C₄	—	8	4	no	—
228	C₂×C₃×C₄	C₂²⋊Q₈	1	4	yes	—
229	C₂×C₃×C₄	C₂²⋊Q₈	1	8	yes	—
230	C₂×C₃×C₄	C₂²×D₄	1	8	yes	—
231	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
233	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
234	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
235	C₂×C₃×C₄	C₂×#41	1	4	yes	—
236	C₂×C₃×C₄	C₂×#41	1	2	yes	—
237	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
238	C₃×C₈	—	2	8	no	—
239	C₂⁴	—	2	2	no	—
240	C₂⁴	—	2	8	no	—
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	8	4	no	—
243	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×Q₈	—	2	8	no	—
245	C₂×D₄	—	2	8	no	—
246	C₂×D₄	—	2	16	no	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	—	2	4	no	—
249	C₂×D₄	—	2	8	no	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	C₂×C₃×Q₈	1	8	yes	—
252	C₂×D₄	C₂×C₃×Q₈	1	16	yes	—
253	C₂×D₄	C₂⁴×C₃	1	4	yes	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	16	no	—
257	C₂²×C₄	—	8	8	no	—
258	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
259	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
261	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
262	C₂²×C₄	C₃×#41	1	4	yes	—
263	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
264	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
265	M₁₆	—	2	8	no	—
266	M₁₆	—	2	8	no	—
267	C₂×C₈	—	2	8	no	—
268	C₂×C₈	C₂⁴×C₃	1	8	yes	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	2	8	no	—
272	C₄⋊C₄	—	2	16	no	—
273	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
274	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
275	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
276	C₂²⋊C₄	—	2	4	no	—
277	C₂²⋊C₄	—	2	4	no	—
278	C₂²⋊C₄	—	2	4	no	—
279	C₂²⋊C₄	—	2	16	no	—
280	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
281	C₄²	—	2	4	no	—
282	C₄²	—	2	4	no	—
283	C₄²	—	2	4	no	—
284	C₄²	C₂×C₃×D₄	1	4	yes	—
285	C₄²	C₂⁴×C₃	1	4	yes	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	2	8	no	—
289	C₂²×C₃	—	4	4	no	—
290	C₂²×C₃	—	4	16	no	—
291	C₂²×C₃	—	4	8	no	—
292	C₂²×C₃	—	8	16	no	—
293	C₂²×C₃	C₂×C₂²⋊Q₈	1	2	yes	—
294	C₂²×C₃	C₂×C₂²⋊Q₈	1	4	yes	—
295	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
296	C₃×C₄	—	2	8	no	—
297	C₃×C₄	—	4	4	no	—
298	C₃×C₄	—	4	8	no	—
299	C₃×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
300	C₃×C₄	C₂×C₂²⋊Q₈	1	4	yes	—
301	C₃×C₄	C₂³×Q₈	1	1	yes	characteristic
302	C₃×C₄	C₂²×#41	1	1	yes	characteristic
303	C₂³	—	2	4	no	—
304	C₂³	—	2	8	no	—
305	C₂³	—	2	16	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	4	8	no	—
308	C₂³	—	8	8	no	—
309	C₂³	—	8	16	no	—
310	C₂³	C₃×C₂²⋊Q₈	1	4	yes	—
311	C₂³	C₂²×C₃×D₄	1	2	yes	—
312	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
313	Q₈	—	8	8	no	—
314	D₄	—	2	4	no	—
315	D₄	—	2	8	no	—
316	D₄	—	2	16	no	—
317	D₄	C₂²×C₃×Q₈	1	8	yes	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	8	16	no	—
323	C₂×C₄	—	8	4	no	—
324	C₂×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
325	C₂×C₄	C₃×C₂²⋊Q₈	1	8	yes	—
326	C₂×C₄	C₂²×C₃×D₄	1	8	yes	—
327	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
329	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
330	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
331	C₂×C₄	C₂×C₃×#41	1	4	yes	—
332	C₂×C₄	C₂×C₃×#41	1	2	yes	—
333	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
334	C₈	—	2	8	no	—
335	C₂×C₃	—	2	2	no	—
336	C₂×C₃	—	2	4	no	—
337	C₂×C₃	—	4	8	no	—
338	C₂×C₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
339	C₂×C₃	#3585	1	2	yes	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	8	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	4	16	no	—
345	C₂²	—	4	8	no	—
346	C₂²	—	8	16	no	—
347	C₂²	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
348	C₂²	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
349	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
350	C₄	—	2	8	no	—
351	C₄	—	4	4	no	—
352	C₄	—	4	8	no	—
353	C₄	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
354	C₄	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
355	C₄	C₂³×C₃×Q₈	1	1	yes	characteristic
356	C₄	C₂²×C₃×#41	1	1	yes	characteristic
357	C₃	#60490	1	1	yes	characteristic, direct product factor, Sylow
358	C₂	—	2	2	no	—
359	C₂	—	2	4	no	—
360	C₂	—	4	8	no	—
361	C₂	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic
362	C₂	C₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3458	C₂	semidirect
3. C₃×#3081	C₂	semidirect
4. C₃×#3077	C₂	semidirect
5. C₃×#2911	C₂	semidirect
6. C₃×#2905	C₂	semidirect
8. #60490	C₃	direct (N × H)
12. C₃×#544	C₂²	semidirect
15. C₃×#533	C₂²	semidirect
24. C₃×#478	C₂²	semidirect
25. C₃×#476	C₂²	semidirect
26. C₃×#474	C₂²	semidirect
27. C₃×#428	C₂²	semidirect
28. C₃×#428	C₂²	semidirect
29. C₃×#427	C₂²	semidirect
30. C₃×#424	C₂²	semidirect
31. C₃×#423	C₂²	semidirect
35. #3458	C₂×C₃	semidirect
37. #3081	C₂×C₃	semidirect
38. #3077	C₂×C₃	semidirect
39. #2911	C₂×C₃	semidirect
40. #2905	C₂×C₃	semidirect
46. C₂²×C₃×D₄	Q₈	semidirect
56. C₃×C₄⋊Q₈	C₂³	semidirect
58. C₃×#125	C₂³	semidirect
84. C₃×#107	C₂³	semidirect
85. C₃×#106	C₂³	semidirect
86. C₃×C₄⋊C₈	C₂³	semidirect
91. #544	C₂²×C₃	semidirect
94. #533	C₂²×C₃	semidirect
103. #478	C₂²×C₃	semidirect
104. #476	C₂²×C₃	semidirect
105. #474	C₂²×C₃	semidirect
106. #428	C₂²×C₃	semidirect
107. #428	C₂²×C₃	semidirect
108. #427	C₂²×C₃	semidirect
109. #424	C₂²×C₃	semidirect
110. #423	C₂²×C₃	semidirect
165. C₂²×D₄	C₃×Q₈	semidirect
175. C₄⋊Q₈	C₂³×C₃	semidirect
177. #125	C₂³×C₃	semidirect
203. #107	C₂³×C₃	semidirect
204. #106	C₂³×C₃	semidirect
205. C₄⋊C₈	C₂³×C₃	semidirect
357. C₃	#60490	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×#3458	2
C₂×C₃×#518	2
C₃×#3081	2
C₃×#3077	2
C₃×#2911	2
C₃×#2905	2
C₂×C₃×#418	2
#60490	3

Subgroups — C3×#60490 #10679097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60490 #10679097