Subgroups — C₃×#34480 #10653087

Order 768.

2436 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₃×#2376	C₂	1	4	yes	maximal, complemented
3	C₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2363	C₂	1	2	yes	maximal, complemented
5	C₃×#2360	C₂	1	2	yes	maximal, complemented
6	C₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2345	C₂	1	2	yes	maximal, complemented
9	C₃×#2341	C₂	1	2	yes	maximal, complemented
10	C₃×#2335	C₂	1	4	yes	maximal, complemented
11	C₃×#2324	C₂	1	2	yes	maximal, complemented
12	C₃×#2323	C₂	1	2	yes	maximal, complemented
13	C₃×#2316	C₂	1	2	yes	maximal, complemented
14	C₃×#2311	C₂	1	2	yes	maximal, complemented
15	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
18	#34480	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	2	yes	—
20	C₃×#547	C₄	1	16	yes	complemented
21	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×#123	C₂²	1	4	yes	—
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₃×#121	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
26	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
27	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
28	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×#117	C₂²	1	2	yes	—
31	C₂×C₃×#117	C₂²	1	2	yes	—
32	C₂×C₃×#117	C₂²	1	2	yes	—
33	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₃×#391	C₂²	1	2	yes	—
36	C₃×#391	C₂²	1	2	yes	—
37	C₃×#390	C₂²	1	1	yes	characteristic
38	C₃×#390	C₂²	1	4	yes	—
39	C₃×#390	C₂²	1	4	yes	—
40	C₃×#390	C₂²	1	1	yes	characteristic
41	C₃×#390	C₂²	1	1	yes	characteristic
42	C₃×#390	C₂²	1	1	yes	characteristic
43	C₃×#390	C₂²	1	2	yes	—
44	C₃×#389	C₂²	1	1	yes	characteristic
45	C₃×#389	C₂²	1	4	yes	—
46	C₃×#389	C₂²	1	2	yes	—
47	C₃×#389	C₂²	1	2	yes	—
48	C₃×#389	C₂²	1	1	yes	characteristic
49	C₃×#389	C₂²	1	1	yes	characteristic
50	C₃×#389	C₂²	1	1	yes	characteristic
51	C₃×#389	C₂²	1	2	yes	—
52	C₃×#389	C₂²	1	4	yes	—
53	C₃×#389	C₂²	1	2	yes	—
54	C₃×#388	C₂²	1	4	yes	—
55	C₃×#388	C₂²	1	2	yes	—
56	C₃×#388	C₂²	1	2	yes	—
57	C₃×#388	C₂²	1	4	yes	—
58	C₃×#388	C₂²	1	2	yes	—
59	C₃×#388	C₂²	1	2	yes	—
60	C₃×#388	C₂²	1	4	yes	—
61	C₃×#387	C₂²	1	4	yes	—
62	C₃×#387	C₂²	1	4	yes	—
63	C₃×#387	C₂²	1	4	yes	—
64	C₃×#386	C₂²	1	4	yes	—
65	C₃×#386	C₂²	1	4	yes	—
66	C₃×#385	C₂²	1	4	yes	—
67	C₃×#385	C₂²	1	4	yes	—
68	C₃×#384	C₂²	1	1	yes	characteristic
69	C₃×#380	C₂²	1	4	yes	—
70	C₃×#380	C₂²	1	4	yes	—
71	C₃×#380	C₂²	1	4	yes	—
72	C₃×#380	C₂²	1	2	yes	—
73	C₃×#380	C₂²	1	2	yes	—
74	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
75	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
76	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
79	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
80	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
83	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
84	C₃×C₄³	C₂²	1	1	yes	characteristic
85	C₂×#547	C₂×C₃	1	1	yes	characteristic
86	#2376	C₂×C₃	1	4	yes	complemented
87	#2365	C₂×C₃	1	1	yes	characteristic, complemented
88	#2363	C₂×C₃	1	2	yes	complemented
89	#2360	C₂×C₃	1	2	yes	complemented
90	#2354	C₂×C₃	1	1	yes	characteristic, complemented
91	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
92	#2345	C₂×C₃	1	2	yes	complemented
93	#2341	C₂×C₃	1	2	yes	complemented
94	#2335	C₂×C₃	1	4	yes	complemented
95	#2324	C₂×C₃	1	2	yes	complemented
96	#2323	C₂×C₃	1	2	yes	complemented
97	#2316	C₂×C₃	1	2	yes	complemented
98	#2311	C₂×C₃	1	2	yes	complemented
99	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
100	#2293	C₂×C₃	1	1	yes	characteristic, complemented
101	#2293	C₂×C₃	1	1	yes	characteristic, complemented
102	C₂×C₃×#41	—	4	4	no	—
103	C₂×C₃×#41	—	4	4	no	—
104	C₂×C₃×#41	C₂×C₄	1	16	yes	complemented
105	C₂²×C₃×Q₈	C₂³	1	2	yes	—
106	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
107	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
108	C₂²×C₃×D₄	C₂³	1	4	yes	—
109	C₂³×C₃×C₄	C₂³	1	2	yes	—
110	C₂³×C₃×C₄	C₂³	1	2	yes	—
111	C₂³×C₃×C₄	C₂³	1	4	yes	—
112	C₂³×C₃×C₄	C₂³	1	4	yes	—
113	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
114	C₃×#123	C₂×C₄	1	32	yes	complemented
115	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
116	C₃×#121	C₂×C₄	1	16	yes	—
117	C₃×C₄×Q₈	—	4	4	no	—
118	C₃×C₄×Q₈	—	4	4	no	—
119	C₃×C₄×D₄	—	4	4	no	—
120	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
121	C₃×C₄×D₄	C₂×C₄	1	8	yes	complemented
122	C₃×#117	—	4	4	no	—
123	C₃×#117	—	4	4	no	—
124	C₃×#117	—	4	4	no	—
125	C₂×C₃×C₄⋊C₄	—	4	4	no	—
126	C₂×C₃×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
127	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₄²	C₂³	1	2	yes	—
166	C₂×C₃×C₄²	C₂³	1	2	yes	—
167	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄²	C₂³	1	4	yes	—
169	C₂×C₃×C₄²	C₂³	1	4	yes	—
170	C₂×C₃×C₄²	C₂³	1	4	yes	—
171	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
172	C₃×#95	C₂³	1	2	yes	—
173	C₃×#95	C₂³	1	2	yes	—
174	C₃×#95	C₂³	1	4	yes	—
175	C₃×#95	C₂³	1	2	yes	—
176	C₃×#95	C₂³	1	4	yes	—
177	C₃×#95	C₂³	1	2	yes	—
178	C₃×#95	C₂³	1	4	yes	—
179	C₃×#95	C₂³	1	4	yes	—
180	C₃×#95	C₂³	1	4	yes	—
181	C₃×#95	C₂³	1	4	yes	—
182	C₃×#95	C₂³	1	2	yes	—
183	C₃×#95	C₂³	1	2	yes	—
184	C₂²×#41	C₂²×C₃	1	2	yes	—
185	#547	C₃×C₄	1	16	yes	complemented
186	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
187	C₂×#123	C₂²×C₃	1	4	yes	—
188	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
189	C₂×#121	C₂²×C₃	1	2	yes	—
190	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
191	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
192	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
193	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
195	C₂×#117	C₂²×C₃	1	2	yes	—
196	C₂×#117	C₂²×C₃	1	2	yes	—
197	C₂×#117	C₂²×C₃	1	2	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
199	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
200	#391	C₂²×C₃	1	2	yes	—
201	#391	C₂²×C₃	1	2	yes	—
202	#390	C₂²×C₃	1	1	yes	characteristic
203	#390	C₂²×C₃	1	2	yes	—
204	#390	C₂²×C₃	1	1	yes	characteristic
205	#390	C₂²×C₃	1	4	yes	—
206	#390	C₂²×C₃	1	4	yes	—
207	#390	C₂²×C₃	1	1	yes	characteristic
208	#390	C₂²×C₃	1	1	yes	characteristic
209	#389	C₂²×C₃	1	2	yes	—
210	#389	C₂²×C₃	1	2	yes	—
211	#389	C₂²×C₃	1	1	yes	characteristic
212	#389	C₂²×C₃	1	4	yes	—
213	#389	C₂²×C₃	1	2	yes	—
214	#389	C₂²×C₃	1	4	yes	—
215	#389	C₂²×C₃	1	2	yes	—
216	#389	C₂²×C₃	1	1	yes	characteristic
217	#389	C₂²×C₃	1	1	yes	characteristic
218	#389	C₂²×C₃	1	1	yes	characteristic
219	#388	C₂²×C₃	1	4	yes	—
220	#388	C₂²×C₃	1	4	yes	—
221	#388	C₂²×C₃	1	2	yes	—
222	#388	C₂²×C₃	1	2	yes	—
223	#388	C₂²×C₃	1	4	yes	—
224	#388	C₂²×C₃	1	2	yes	—
225	#388	C₂²×C₃	1	2	yes	—
226	#387	C₂²×C₃	1	4	yes	—
227	#387	C₂²×C₃	1	4	yes	—
228	#387	C₂²×C₃	1	4	yes	—
229	#386	C₂²×C₃	1	4	yes	—
230	#386	C₂²×C₃	1	4	yes	—
231	#385	C₂²×C₃	1	4	yes	—
232	#385	C₂²×C₃	1	4	yes	—
233	#384	C₂²×C₃	1	1	yes	characteristic
234	#380	C₂²×C₃	1	4	yes	—
235	#380	C₂²×C₃	1	4	yes	—
236	#380	C₂²×C₃	1	4	yes	—
237	#380	C₂²×C₃	1	2	yes	—
238	#380	C₂²×C₃	1	2	yes	—
239	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
240	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
241	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
242	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
243	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
244	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
245	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
246	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
247	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
248	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
249	C₄³	C₂²×C₃	1	1	yes	characteristic
250	C₂⁴×C₃	C₂⁴	1	2	yes	—
251	C₂⁴×C₃	C₂⁴	1	2	yes	—
252	C₃×#41	—	4	32	no	—
253	C₂×C₃×Q₈	—	2	4	no	—
254	C₂×C₃×Q₈	—	2	4	no	—
255	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
256	C₂×C₃×D₄	—	2	2	no	—
257	C₂×C₃×D₄	—	2	2	no	—
258	C₂×C₃×D₄	—	2	2	no	—
259	C₂×C₃×D₄	—	2	2	no	—
260	C₂×C₃×D₄	—	4	4	no	—
261	C₂×C₃×D₄	—	4	4	no	—
262	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
263	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
264	C₂×C₃×D₄	C₂²×C₄	1	16	yes	—
265	C₂²×C₃×C₄	—	2	4	no	—
266	C₂²×C₃×C₄	—	2	4	no	—
267	C₂²×C₃×C₄	—	2	4	no	—
268	C₂²×C₃×C₄	—	2	4	no	—
269	C₂²×C₃×C₄	—	4	4	no	—
270	C₂²×C₃×C₄	—	4	4	no	—
271	C₂²×C₃×C₄	—	4	4	no	—
272	C₂²×C₃×C₄	—	4	4	no	—
273	C₂²×C₃×C₄	—	4	4	no	—
274	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
275	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
276	C₂²×C₃×C₄	C₂²×C₄	1	16	yes	—
277	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
278	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
279	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
280	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
281	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
283	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
284	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
287	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
288	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
289	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
290	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
291	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
292	C₃×C₄⋊C₄	—	2	2	no	—
293	C₃×C₄⋊C₄	—	2	4	no	—
294	C₃×C₄⋊C₄	—	2	2	no	—
295	C₃×C₄⋊C₄	—	2	4	no	—
296	C₃×C₄⋊C₄	—	2	2	no	—
297	C₃×C₄⋊C₄	—	2	2	no	—
298	C₃×C₄⋊C₄	—	4	4	no	—
299	C₃×C₄⋊C₄	—	4	2	no	—
300	C₃×C₄⋊C₄	—	4	2	no	—
301	C₃×C₄⋊C₄	—	4	2	no	—
302	C₃×C₄⋊C₄	—	4	2	no	—
303	C₃×C₄⋊C₄	—	4	2	no	—
304	C₃×C₄⋊C₄	—	4	4	no	—
305	C₃×C₄⋊C₄	—	4	4	no	—
306	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
307	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
308	C₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
309	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
310	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
311	C₃×C₂²⋊C₄	—	2	4	no	—
312	C₃×C₂²⋊C₄	—	2	4	no	—
313	C₃×C₂²⋊C₄	—	4	2	no	—
314	C₃×C₂²⋊C₄	—	4	2	no	—
315	C₃×C₂²⋊C₄	—	4	4	no	—
316	C₃×C₂²⋊C₄	—	4	2	no	—
317	C₃×C₂²⋊C₄	—	4	2	no	—
318	C₃×C₂²⋊C₄	—	4	2	no	—
319	C₃×C₂²⋊C₄	—	4	2	no	—
320	C₃×C₂²⋊C₄	—	4	4	no	—
321	C₃×C₂²⋊C₄	—	4	4	no	—
322	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
323	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
324	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
325	C₃×C₄²	—	2	2	no	—
326	C₃×C₄²	—	2	2	no	—
327	C₃×C₄²	—	2	4	no	—
328	C₃×C₄²	—	2	4	no	—
329	C₃×C₄²	—	2	2	no	—
330	C₃×C₄²	—	2	2	no	—
331	C₃×C₄²	—	2	2	no	—
332	C₃×C₄²	—	4	1	no	—
333	C₃×C₄²	—	4	4	no	—
334	C₃×C₄²	—	4	4	no	—
335	C₃×C₄²	—	4	4	no	—
336	C₃×C₄²	C₂²×C₄	1	4	yes	—
337	C₂×#41	—	4	4	no	—
338	C₂×#41	—	4	4	no	—
339	C₂×#41	C₂×C₃×C₄	1	16	yes	complemented
340	C₂²×Q₈	C₂³×C₃	1	2	yes	—
341	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
343	C₂²×D₄	C₂³×C₃	1	4	yes	—
344	C₂³×C₄	C₂³×C₃	1	2	yes	—
345	C₂³×C₄	C₂³×C₃	1	2	yes	—
346	C₂³×C₄	C₂³×C₃	1	4	yes	—
347	C₂³×C₄	C₂³×C₃	1	4	yes	—
348	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
349	#123	C₂×C₃×C₄	1	32	yes	complemented
350	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
351	#121	C₂×C₃×C₄	1	16	yes	—
352	C₄×Q₈	—	4	4	no	—
353	C₄×Q₈	—	4	4	no	—
354	C₄×D₄	—	4	4	no	—
355	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
356	C₄×D₄	C₂×C₃×C₄	1	8	yes	complemented
357	#117	—	4	4	no	—
358	#117	—	4	4	no	—
359	#117	—	4	4	no	—
360	C₂×C₄⋊C₄	—	4	4	no	—
361	C₂×C₄⋊C₄	C₂×C₃×C₄	1	16	yes	complemented
362	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
395	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₃	1	2	yes	—
398	C₂×C₄²	C₂³×C₃	1	2	yes	—
399	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₃	1	4	yes	—
403	C₂×C₄²	C₂³×C₃	1	4	yes	—
404	C₂×C₄²	C₂³×C₃	1	4	yes	—
405	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
407	#95	C₂³×C₃	1	2	yes	—
408	#95	C₂³×C₃	1	2	yes	—
409	#95	C₂³×C₃	1	4	yes	—
410	#95	C₂³×C₃	1	2	yes	—
411	#95	C₂³×C₃	1	4	yes	—
412	#95	C₂³×C₃	1	2	yes	—
413	#95	C₂³×C₃	1	4	yes	—
414	#95	C₂³×C₃	1	4	yes	—
415	#95	C₂³×C₃	1	4	yes	—
416	#95	C₂³×C₃	1	4	yes	—
417	#95	C₂³×C₃	1	2	yes	—
418	#95	C₂³×C₃	1	2	yes	—
419	C₂³×C₃	—	2	2	no	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	—	2	2	no	—
422	C₂³×C₃	—	2	2	no	—
423	C₂³×C₃	—	2	2	no	—
424	C₂³×C₃	—	2	2	no	—
425	C₂³×C₃	—	2	2	no	—
426	C₂³×C₃	—	2	2	no	—
427	C₂³×C₃	—	2	2	no	—
428	C₂³×C₃	—	2	2	no	—
429	C₂³×C₃	—	2	2	no	—
430	C₂³×C₃	—	2	2	no	—
431	C₂³×C₃	C₂³×C₄	1	4	yes	—
432	C₂³×C₃	C₂³×C₄	1	4	yes	—
433	C₂³×C₃	C₂⁵	1	1	yes	characteristic
434	C₃×Q₈	—	2	16	no	—
435	C₃×D₄	—	2	8	no	—
436	C₃×D₄	—	2	8	no	—
437	C₃×D₄	—	4	16	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	2	no	—
440	C₂×C₃×C₄	—	2	4	no	—
441	C₂×C₃×C₄	—	2	4	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	2	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	2	no	—
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	16	no	—
449	C₂×C₃×C₄	—	2	16	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	2	2	no	—
457	C₂×C₃×C₄	—	2	2	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	2	no	—
460	C₂×C₃×C₄	—	2	2	no	—
461	C₂×C₃×C₄	—	2	4	no	—
462	C₂×C₃×C₄	—	2	4	no	—
463	C₂×C₃×C₄	—	2	2	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	2	no	—
467	C₂×C₃×C₄	—	2	2	no	—
468	C₂×C₃×C₄	—	2	2	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	2	no	—
472	C₂×C₃×C₄	—	2	4	no	—
473	C₂×C₃×C₄	—	2	2	no	—
474	C₂×C₃×C₄	—	4	16	no	—
475	C₂×C₃×C₄	—	8	8	no	—
476	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
477	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
478	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
479	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
480	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
481	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
482	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
483	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
484	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
485	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
486	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
487	C₂⁴	C₂⁴×C₃	1	2	yes	—
488	C₂⁴	C₂⁴×C₃	1	2	yes	—
489	#41	—	4	32	no	—
490	C₂×Q₈	—	2	4	no	—
491	C₂×Q₈	—	2	4	no	—
492	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	4	4	no	—
498	C₂×D₄	—	4	4	no	—
499	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
500	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
501	C₂×D₄	C₂²×C₃×C₄	1	16	yes	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	4	4	no	—
507	C₂²×C₄	—	4	4	no	—
508	C₂²×C₄	—	4	4	no	—
509	C₂²×C₄	—	4	4	no	—
510	C₂²×C₄	—	4	4	no	—
511	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
512	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
513	C₂²×C₄	C₂²×C₃×C₄	1	16	yes	—
514	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	4	4	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
544	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
545	C₄⋊C₄	C₂²×C₃×C₄	1	16	yes	—
546	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
547	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	4	2	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	4	4	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
560	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
561	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
562	C₄²	—	2	2	no	—
563	C₄²	—	2	2	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	4	4	no	—
570	C₄²	—	4	4	no	—
571	C₄²	—	4	4	no	—
572	C₄²	—	4	1	no	—
573	C₄²	C₂²×C₃×C₄	1	4	yes	—
574	C₂²×C₃	—	2	4	no	—
575	C₂²×C₃	—	2	4	no	—
576	C₂²×C₃	—	2	4	no	—
577	C₂²×C₃	—	2	4	no	—
578	C₂²×C₃	—	2	4	no	—
579	C₂²×C₃	—	2	4	no	—
580	C₂²×C₃	—	4	2	no	—
581	C₂²×C₃	—	4	2	no	—
582	C₂²×C₃	—	4	2	no	—
583	C₂²×C₃	—	4	2	no	—
584	C₂²×C₃	—	4	2	no	—
585	C₂²×C₃	—	4	2	no	—
586	C₂²×C₃	—	4	2	no	—
587	C₂²×C₃	—	4	2	no	—
588	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
589	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
593	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
594	C₂²×C₃	#585	1	1	yes	characteristic
595	C₃×C₄	—	2	4	no	—
596	C₃×C₄	—	2	8	no	—
597	C₃×C₄	—	2	4	no	—
598	C₃×C₄	—	2	2	no	—
599	C₃×C₄	—	2	2	no	—
600	C₃×C₄	—	4	1	no	—
601	C₃×C₄	—	4	4	no	—
602	C₃×C₄	—	4	2	no	—
603	C₃×C₄	—	4	2	no	—
604	C₃×C₄	—	4	1	no	—
605	C₃×C₄	—	4	2	no	—
606	C₃×C₄	—	4	1	no	—
607	C₃×C₄	—	4	2	no	—
608	C₃×C₄	#518	1	4	yes	—
609	C₃×C₄	#520	1	4	yes	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	C₂³×C₃×C₄	1	4	yes	—
623	C₂³	C₂³×C₃×C₄	1	4	yes	—
624	C₂³	C₂⁵×C₃	1	1	yes	characteristic
625	Q₈	—	2	16	no	—
626	D₄	—	2	8	no	—
627	D₄	—	2	8	no	—
628	D₄	—	4	16	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	16	no	—
640	C₂×C₄	—	2	16	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	4	16	no	—
666	C₂×C₄	—	8	8	no	—
667	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
668	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
669	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
670	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
671	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
672	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
673	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
674	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
675	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
676	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
677	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
678	C₂×C₃	—	4	4	no	—
679	C₂×C₃	—	4	4	no	—
680	C₂×C₃	C₂×#518	1	1	yes	characteristic
681	C₂×C₃	C₂×#520	1	1	yes	characteristic
682	C₂×C₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
683	C₂×C₃	#3546	1	1	yes	characteristic
684	C₂×C₃	#3547	1	1	yes	characteristic
685	C₂×C₃	#3548	1	1	yes	characteristic
686	C₂×C₃	#3552	1	1	yes	characteristic
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
702	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
706	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
707	C₂²	C₃×#585	1	1	yes	characteristic
708	C₄	—	2	4	no	—
709	C₄	—	2	8	no	—
710	C₄	—	2	4	no	—
711	C₄	—	2	2	no	—
712	C₄	—	2	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	4	no	—
715	C₄	—	4	1	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	2	no	—
721	C₄	C₃×#518	1	4	yes	—
722	C₄	C₃×#520	1	4	yes	—
723	C₃	#34480	1	1	yes	characteristic, direct product factor, Sylow
724	C₂	—	4	4	no	—
725	C₂	—	4	4	no	—
726	C₂	C₂×C₃×#518	1	1	yes	characteristic
727	C₂	C₂×C₃×#520	1	1	yes	characteristic
728	C₂	C₃×C₄×2₋¹⁺⁴	1	1	yes	characteristic
729	C₂	C₃×#3546	1	1	yes	characteristic
730	C₂	C₃×#3547	1	1	yes	characteristic
731	C₂	C₃×#3548	1	1	yes	characteristic
732	C₂	C₃×#3552	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#547	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2376	C₂	semidirect
3. C₃×#2365	C₂	semidirect
4. C₃×#2363	C₂	semidirect
5. C₃×#2360	C₂	semidirect
6. C₃×#2354	C₂	semidirect
7. C₃×D₄×C₄⋊C₄	C₂	semidirect
8. C₃×#2345	C₂	semidirect
9. C₃×#2341	C₂	semidirect
10. C₃×#2335	C₂	semidirect
11. C₃×#2324	C₂	semidirect
12. C₃×#2323	C₂	semidirect
13. C₃×#2316	C₂	semidirect
14. C₃×#2311	C₂	semidirect
15. C₃×C₄×C₄⋊Q₈	C₂	semidirect
16. C₃×#2293	C₂	semidirect
17. C₃×#2293	C₂	semidirect
18. #34480	C₃	direct (N × H)
20. C₃×#547	C₄	semidirect
86. #2376	C₂×C₃	semidirect
87. #2365	C₂×C₃	semidirect
88. #2363	C₂×C₃	semidirect
89. #2360	C₂×C₃	semidirect
90. #2354	C₂×C₃	semidirect
91. D₄×C₄⋊C₄	C₂×C₃	semidirect
92. #2345	C₂×C₃	semidirect
93. #2341	C₂×C₃	semidirect
94. #2335	C₂×C₃	semidirect
95. #2324	C₂×C₃	semidirect
96. #2323	C₂×C₃	semidirect
97. #2316	C₂×C₃	semidirect
98. #2311	C₂×C₃	semidirect
99. C₄×C₄⋊Q₈	C₂×C₃	semidirect
100. #2293	C₂×C₃	semidirect
101. #2293	C₂×C₃	semidirect
104. C₂×C₃×#41	C₂×C₄	semidirect
113. C₃×C₄⋊Q₈	C₂×C₄	semidirect
114. C₃×#123	C₂×C₄	semidirect
115. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
121. C₃×C₄×D₄	C₂×C₄	semidirect
126. C₂×C₃×C₄⋊C₄	C₂×C₄	semidirect
185. #547	C₃×C₄	semidirect
339. C₂×#41	C₂×C₃×C₄	semidirect
348. C₄⋊Q₈	C₂×C₃×C₄	semidirect
349. #123	C₂×C₃×C₄	semidirect
350. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
356. C₄×D₄	C₂×C₃×C₄	semidirect
361. C₂×C₄⋊C₄	C₂×C₃×C₄	semidirect
723. C₃	#34480	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#547	2
C₃×#2376	2
C₃×#2365	2
C₃×#2363	2
C₃×#2360	2
C₃×#2354	2
C₃×D₄×C₄⋊C₄	2
C₃×#2345	2
C₃×#2341	2
C₃×#2335	2
C₃×#2324	2
C₃×#2323	2
C₃×#2316	2
C₃×#2311	2
C₃×C₄×C₄⋊Q₈	2
C₃×#2293	2
#34480	3

Subgroups — C3×#34480 #10653087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34480 #10653087