Subgroups — C₃×#3521 #87405

Order 384.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#553	C₂	1	2	yes	maximal, complemented
6	C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#552	C₂	1	2	yes	maximal, complemented
8	C₃×#551	C₂	1	2	yes	maximal, complemented
9	C₃×#551	C₂	1	2	yes	maximal, complemented
10	C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#539	C₂	1	2	yes	maximal, complemented
16	C₃×#538	C₂	1	2	yes	maximal, complemented
17	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#529	C₂	1	2	yes	maximal, complemented
19	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃×#126	C₂	1	2	yes	maximal, complemented
21	C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
24	#3521	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×#41	C₂²	1	1	yes	characteristic
27	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃×#126	C₂²	1	1	yes	characteristic
31	C₃×#126	C₂²	1	2	yes	—
32	C₃×#126	C₂²	1	2	yes	—
33	C₃×#126	C₂²	1	2	yes	—
34	C₃×#126	C₂²	1	2	yes	—
35	C₃×#126	C₂²	1	2	yes	complemented
36	C₃×#126	C₂²	1	2	yes	complemented
37	C₃×#126	C₂²	1	2	yes	complemented
38	C₃×#126	C₂²	1	2	yes	complemented
39	C₃×#126	C₂²	1	1	yes	characteristic, complemented
40	C₃×#126	C₂²	1	2	yes	complemented
41	C₃×#126	C₂²	1	2	yes	complemented
42	C₃×#125	C₂²	1	2	yes	complemented
43	C₃×#125	C₂²	1	1	yes	characteristic, complemented
44	C₃×#125	C₂²	1	1	yes	characteristic, complemented
45	C₃×#125	C₂²	1	2	yes	complemented
46	C₃×#125	C₂²	1	2	yes	complemented
47	C₃×#125	C₂²	1	1	yes	characteristic, complemented
48	C₃×#124	C₂²	1	1	yes	characteristic
49	C₃×#124	C₂²	1	1	yes	characteristic
50	C₃×#124	C₂²	1	2	yes	—
51	C₃×#124	C₂²	1	1	yes	characteristic
52	C₃×#124	C₂²	1	2	yes	complemented
53	C₃×#123	C₂²	1	2	yes	—
54	C₃×#123	C₂²	1	1	yes	characteristic
55	C₃×#123	C₂²	1	2	yes	—
56	C₃×#123	C₂²	1	2	yes	—
57	C₃×#123	C₂²	1	2	yes	complemented
58	C₃×#123	C₂²	1	2	yes	complemented
59	C₃×#123	C₂²	1	1	yes	characteristic, complemented
60	C₃×#123	C₂²	1	2	yes	complemented
61	C₃×#123	C₂²	1	2	yes	complemented
62	C₃×#123	C₂²	1	2	yes	complemented
63	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
64	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
65	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
66	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
67	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
69	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
70	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
71	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
72	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
73	C₃×#121	C₂²	1	1	yes	characteristic
74	C₃×#121	C₂²	1	1	yes	characteristic
75	C₃×#121	C₂²	1	2	yes	—
76	C₃×#121	C₂²	1	2	yes	—
77	C₃×#121	C₂²	1	1	yes	characteristic
78	C₃×#121	C₂²	1	2	yes	complemented
79	C₃×#121	C₂²	1	2	yes	complemented
80	C₃×#120	C₂²	1	2	yes	—
81	C₃×#120	C₂²	1	2	yes	—
82	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
84	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
87	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
88	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
89	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
90	C₃×C₄×D₄	C₂²	1	2	yes	—
91	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
92	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
93	C₃×C₄×D₄	C₂²	1	2	yes	—
94	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
95	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
96	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
97	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
98	C₃×C₄×D₄	C₂²	1	2	yes	complemented
99	C₃×C₄×D₄	C₂²	1	2	yes	complemented
100	C₃×C₄×D₄	C₂²	1	2	yes	complemented
101	C₃×C₄×D₄	C₂²	1	2	yes	complemented
102	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
103	C₃×C₄×D₄	C₂²	1	2	yes	complemented
104	C₃×C₄×D₄	C₂²	1	2	yes	complemented
105	C₃×#117	C₂²	1	1	yes	characteristic
106	C₃×#117	C₂²	1	1	yes	characteristic
107	C₃×#117	C₂²	1	2	yes	complemented
108	C₃×#117	C₂²	1	1	yes	characteristic, complemented
109	C₃×#117	C₂²	1	1	yes	characteristic, complemented
110	C₃×#117	C₂²	1	2	yes	complemented
111	C₃×#117	C₂²	1	2	yes	complemented
112	C₃×#117	C₂²	1	2	yes	complemented
113	C₃×#117	C₂²	1	2	yes	complemented
114	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
115	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
117	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
118	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₂×C₃×C₄²	C₂²	1	2	yes	complemented
123	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
124	#556	C₂×C₃	1	1	yes	characteristic, complemented
125	#556	C₂×C₃	1	1	yes	characteristic, complemented
126	#554	C₂×C₃	1	1	yes	characteristic, complemented
127	#553	C₂×C₃	1	1	yes	characteristic, complemented
128	#553	C₂×C₃	1	2	yes	complemented
129	#552	C₂×C₃	1	1	yes	characteristic, complemented
130	#552	C₂×C₃	1	2	yes	complemented
131	#551	C₂×C₃	1	2	yes	complemented
132	#551	C₂×C₃	1	2	yes	complemented
133	#547	C₂×C₃	1	1	yes	characteristic, complemented
134	#546	C₂×C₃	1	1	yes	characteristic, complemented
135	#546	C₂×C₃	1	1	yes	characteristic, complemented
136	#542	C₂×C₃	1	1	yes	characteristic, complemented
137	#541	C₂×C₃	1	1	yes	characteristic, complemented
138	#539	C₂×C₃	1	2	yes	complemented
139	#538	C₂×C₃	1	2	yes	complemented
140	#529	C₂×C₃	1	1	yes	characteristic, complemented
141	#529	C₂×C₃	1	2	yes	complemented
142	#529	C₂×C₃	1	1	yes	characteristic, complemented
143	C₂×#126	C₂×C₃	1	2	yes	complemented
144	#520	C₂×C₃	1	1	yes	characteristic, complemented
145	#518	C₂×C₃	1	1	yes	characteristic, complemented
146	C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₃×#41	—	2	4	no	—
149	C₃×#41	—	2	4	no	—
150	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂×C₃×Q₈	C₂³	1	2	yes	—
154	C₂×C₃×D₄	—	2	4	no	—
155	C₂×C₃×D₄	C₂³	1	2	yes	—
156	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×D₄	C₂³	1	2	yes	—
158	C₂×C₃×D₄	C₂³	1	2	yes	—
159	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
160	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×D₄	C₂³	1	2	yes	—
162	C₂×C₃×D₄	C₂³	1	2	yes	—
163	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³	1	2	yes	—
166	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂³	1	2	yes	—
168	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂³	1	2	yes	—
171	C₂²×C₃×C₄	C₂³	1	2	yes	—
172	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂³	1	2	yes	—
175	C₂²×C₃×C₄	C₂³	1	2	yes	—
176	C₂²×C₃×C₄	C₂³	1	2	yes	—
177	C₂²×C₃×C₄	C₂³	1	2	yes	—
178	C₂²×C₃×C₄	C₂³	1	2	yes	—
179	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₃×C₄²	C₂³	1	1	yes	characteristic
238	C₃×C₄²	C₂³	1	1	yes	characteristic
239	C₃×C₄²	C₂³	1	1	yes	characteristic
240	C₃×C₄²	C₂³	1	2	yes	—
241	C₃×C₄²	C₂³	1	2	yes	—
242	C₃×C₄²	C₂³	1	1	yes	characteristic
243	C₃×C₄²	C₂³	1	2	yes	—
244	C₃×C₄²	C₂³	1	2	yes	—
245	C₃×C₄²	C₂³	1	1	yes	characteristic
246	C₃×C₄²	C₂³	1	2	yes	—
247	C₃×C₄²	C₂³	1	2	yes	—
248	C₃×C₄²	C₂³	1	1	yes	characteristic
249	C₂×#41	C₂²×C₃	1	1	yes	characteristic
250	C₂×#41	C₂²×C₃	1	1	yes	characteristic
251	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
252	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
253	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
254	#126	C₂²×C₃	1	1	yes	characteristic
255	#126	C₂²×C₃	1	2	yes	—
256	#126	C₂²×C₃	1	2	yes	—
257	#126	C₂²×C₃	1	2	yes	—
258	#126	C₂²×C₃	1	2	yes	—
259	#126	C₂²×C₃	1	2	yes	complemented
260	#126	C₂²×C₃	1	2	yes	complemented
261	#126	C₂²×C₃	1	2	yes	complemented
262	#126	C₂²×C₃	1	2	yes	complemented
263	#126	C₂²×C₃	1	1	yes	characteristic, complemented
264	#126	C₂²×C₃	1	2	yes	complemented
265	#126	C₂²×C₃	1	2	yes	complemented
266	#125	C₂²×C₃	1	2	yes	complemented
267	#125	C₂²×C₃	1	1	yes	characteristic, complemented
268	#125	C₂²×C₃	1	1	yes	characteristic, complemented
269	#125	C₂²×C₃	1	2	yes	complemented
270	#125	C₂²×C₃	1	2	yes	complemented
271	#125	C₂²×C₃	1	1	yes	characteristic, complemented
272	#124	C₂²×C₃	1	1	yes	characteristic
273	#124	C₂²×C₃	1	1	yes	characteristic
274	#124	C₂²×C₃	1	2	yes	—
275	#124	C₂²×C₃	1	1	yes	characteristic
276	#124	C₂²×C₃	1	2	yes	complemented
277	#123	C₂²×C₃	1	2	yes	—
278	#123	C₂²×C₃	1	1	yes	characteristic
279	#123	C₂²×C₃	1	2	yes	—
280	#123	C₂²×C₃	1	2	yes	—
281	#123	C₂²×C₃	1	2	yes	complemented
282	#123	C₂²×C₃	1	2	yes	complemented
283	#123	C₂²×C₃	1	1	yes	characteristic, complemented
284	#123	C₂²×C₃	1	2	yes	complemented
285	#123	C₂²×C₃	1	2	yes	complemented
286	#123	C₂²×C₃	1	2	yes	complemented
287	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
288	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
289	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
290	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
291	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
292	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
293	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
294	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
295	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
297	#121	C₂²×C₃	1	1	yes	characteristic
298	#121	C₂²×C₃	1	1	yes	characteristic
299	#121	C₂²×C₃	1	2	yes	—
300	#121	C₂²×C₃	1	2	yes	—
301	#121	C₂²×C₃	1	1	yes	characteristic
302	#121	C₂²×C₃	1	2	yes	complemented
303	#121	C₂²×C₃	1	2	yes	complemented
304	#120	C₂²×C₃	1	2	yes	—
305	#120	C₂²×C₃	1	2	yes	—
306	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
307	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
308	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
309	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
310	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
311	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
312	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
313	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
314	C₄×D₄	C₂²×C₃	1	2	yes	—
315	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
316	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
317	C₄×D₄	C₂²×C₃	1	2	yes	—
318	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
319	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
320	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
321	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
322	C₄×D₄	C₂²×C₃	1	2	yes	complemented
323	C₄×D₄	C₂²×C₃	1	2	yes	complemented
324	C₄×D₄	C₂²×C₃	1	2	yes	complemented
325	C₄×D₄	C₂²×C₃	1	2	yes	complemented
326	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₄×D₄	C₂²×C₃	1	2	yes	complemented
328	C₄×D₄	C₂²×C₃	1	2	yes	complemented
329	#117	C₂²×C₃	1	1	yes	characteristic
330	#117	C₂²×C₃	1	1	yes	characteristic
331	#117	C₂²×C₃	1	2	yes	complemented
332	#117	C₂²×C₃	1	1	yes	characteristic, complemented
333	#117	C₂²×C₃	1	1	yes	characteristic, complemented
334	#117	C₂²×C₃	1	2	yes	complemented
335	#117	C₂²×C₃	1	2	yes	complemented
336	#117	C₂²×C₃	1	2	yes	complemented
337	#117	C₂²×C₃	1	2	yes	complemented
338	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
339	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
340	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
341	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
342	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
343	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
344	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
346	C₂×C₄²	C₂²×C₃	1	2	yes	complemented
347	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
348	C₂³×C₃	—	2	4	no	—
349	C₂³×C₃	—	4	2	no	—
350	C₂³×C₃	—	4	2	no	—
351	C₂³×C₃	C₂⁴	1	1	yes	characteristic
352	C₂³×C₃	C₂⁴	1	2	yes	—
353	C₂³×C₃	C₂⁴	1	1	yes	characteristic
354	C₂³×C₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₃	C₂⁴	1	2	yes	—
356	C₃×Q₈	—	2	2	no	—
357	C₃×Q₈	—	2	2	no	—
358	C₃×Q₈	—	4	1	no	—
359	C₃×Q₈	—	4	2	no	—
360	C₃×D₄	—	2	4	no	—
361	C₃×D₄	—	2	4	no	—
362	C₃×D₄	—	2	4	no	—
363	C₃×D₄	—	2	2	no	—
364	C₃×D₄	—	4	2	no	—
365	C₃×D₄	—	4	1	no	—
366	C₃×D₄	—	4	1	no	—
367	C₃×D₄	—	4	2	no	—
368	C₃×D₄	—	4	1	no	—
369	C₃×D₄	#41	1	4	yes	—
370	C₂×C₃×C₄	—	2	4	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	4	2	no	—
376	C₂×C₃×C₄	—	4	1	no	—
377	C₂×C₃×C₄	—	4	2	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	—	4	2	no	—
380	C₂×C₃×C₄	—	4	2	no	—
381	C₂×C₃×C₄	—	4	1	no	—
382	C₂×C₃×C₄	—	4	2	no	—
383	C₂×C₃×C₄	—	4	2	no	—
384	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂⁴	1	2	yes	—
389	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂⁴	1	2	yes	—
391	C₂×C₃×C₄	C₂⁴	1	2	yes	—
392	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂⁴	1	2	yes	—
394	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂⁴	1	2	yes	—
396	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂⁴	1	2	yes	—
400	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₂⁴	C₂³×C₃	1	2	yes	—
403	#41	—	2	4	no	—
404	#41	—	2	4	no	—
405	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
406	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
407	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
408	C₂×Q₈	C₂³×C₃	1	2	yes	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	C₂³×C₃	1	2	yes	—
411	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
412	C₂×D₄	C₂³×C₃	1	2	yes	—
413	C₂×D₄	C₂³×C₃	1	2	yes	—
414	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
415	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
416	C₂×D₄	C₂³×C₃	1	2	yes	—
417	C₂×D₄	C₂³×C₃	1	2	yes	—
418	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
419	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
420	C₂²×C₄	C₂³×C₃	1	2	yes	—
421	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
422	C₂²×C₄	C₂³×C₃	1	2	yes	—
423	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
424	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂²×C₄	C₂³×C₃	1	2	yes	—
426	C₂²×C₄	C₂³×C₃	1	2	yes	—
427	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
428	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
429	C₂²×C₄	C₂³×C₃	1	2	yes	—
430	C₂²×C₄	C₂³×C₃	1	2	yes	—
431	C₂²×C₄	C₂³×C₃	1	2	yes	—
432	C₂²×C₄	C₂³×C₃	1	2	yes	—
433	C₂²×C₄	C₂³×C₃	1	2	yes	—
434	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
435	C₄⋊C₄	C₂³×C₃	1	2	yes	—
436	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
437	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
438	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
439	C₄⋊C₄	C₂³×C₃	1	2	yes	—
440	C₄⋊C₄	C₂³×C₃	1	2	yes	—
441	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₄⋊C₄	C₂³×C₃	1	2	yes	—
443	C₄⋊C₄	C₂³×C₃	1	2	yes	—
444	C₄⋊C₄	C₂³×C₃	1	2	yes	—
445	C₄⋊C₄	C₂³×C₃	1	2	yes	—
446	C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₄⋊C₄	C₂³×C₃	1	2	yes	—
448	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
449	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
450	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
451	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
452	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
453	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
454	C₄⋊C₄	C₂³×C₃	1	2	yes	—
455	C₄⋊C₄	C₂³×C₃	1	2	yes	—
456	C₄⋊C₄	C₂³×C₃	1	2	yes	—
457	C₄⋊C₄	C₂³×C₃	1	2	yes	—
458	C₄⋊C₄	C₂³×C₃	1	2	yes	—
459	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
460	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂³×C₃	1	2	yes	—
462	C₄⋊C₄	C₂³×C₃	1	2	yes	—
463	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
464	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
465	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
466	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
467	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
468	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
469	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
470	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
472	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
474	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
477	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
478	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
480	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
483	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
484	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
485	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
489	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
490	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₄²	C₂³×C₃	1	1	yes	characteristic
493	C₄²	C₂³×C₃	1	1	yes	characteristic
494	C₄²	C₂³×C₃	1	1	yes	characteristic
495	C₄²	C₂³×C₃	1	2	yes	—
496	C₄²	C₂³×C₃	1	2	yes	—
497	C₄²	C₂³×C₃	1	1	yes	characteristic
498	C₄²	C₂³×C₃	1	2	yes	—
499	C₄²	C₂³×C₃	1	2	yes	—
500	C₄²	C₂³×C₃	1	1	yes	characteristic
501	C₄²	C₂³×C₃	1	2	yes	—
502	C₄²	C₂³×C₃	1	2	yes	—
503	C₄²	C₂³×C₃	1	1	yes	characteristic
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	2	no	—
514	C₂²×C₃	—	2	2	no	—
515	C₂²×C₃	—	2	1	no	—
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	2	1	no	—
518	C₂²×C₃	—	8	4	no	—
519	C₂²×C₃	C₂×#41	1	4	yes	—
520	C₂²×C₃	C₂⁵	1	1	yes	characteristic
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	2	no	—
525	C₃×C₄	—	2	2	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	2	no	—
528	C₃×C₄	—	2	1	no	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	2	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	2	2	no	—
535	C₃×C₄	—	2	1	no	—
536	C₃×C₄	—	2	2	no	—
537	C₃×C₄	—	2	1	no	—
538	C₃×C₄	C₂×#41	1	2	yes	—
539	C₂³	—	2	4	no	—
540	C₂³	—	4	2	no	—
541	C₂³	—	4	2	no	—
542	C₂³	C₂⁴×C₃	1	1	yes	characteristic
543	C₂³	C₂⁴×C₃	1	2	yes	—
544	C₂³	C₂⁴×C₃	1	1	yes	characteristic
545	C₂³	C₂⁴×C₃	1	1	yes	characteristic
546	C₂³	C₂⁴×C₃	1	2	yes	—
547	Q₈	—	2	2	no	—
548	Q₈	—	2	2	no	—
549	Q₈	—	4	1	no	—
550	Q₈	—	4	2	no	—
551	D₄	—	2	4	no	—
552	D₄	—	2	4	no	—
553	D₄	—	2	4	no	—
554	D₄	—	2	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	1	no	—
560	D₄	C₃×#41	1	4	yes	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
576	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
577	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
578	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
579	C₂×C₄	C₂⁴×C₃	1	2	yes	—
580	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
581	C₂×C₄	C₂⁴×C₃	1	2	yes	—
582	C₂×C₄	C₂⁴×C₃	1	2	yes	—
583	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
584	C₂×C₄	C₂⁴×C₃	1	2	yes	—
585	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
586	C₂×C₄	C₂⁴×C₃	1	2	yes	—
587	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
588	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
589	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
590	C₂×C₄	C₂⁴×C₃	1	2	yes	—
591	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
592	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
593	C₂×C₃	—	2	4	no	—
594	C₂×C₃	—	4	1	no	—
595	C₂×C₃	—	4	1	no	—
596	C₂×C₃	—	4	2	no	—
597	C₂×C₃	—	4	1	no	—
598	C₂×C₃	C₂²×#41	1	1	yes	characteristic
599	C₂×C₃	#585	1	1	yes	characteristic
600	C₂×C₃	#585	1	1	yes	characteristic
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	8	4	no	—
616	C₂²	C₂×C₃×#41	1	4	yes	—
617	C₂²	C₂⁵×C₃	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	C₂×C₃×#41	1	2	yes	—
636	C₃	#3521	1	1	yes	characteristic, direct product factor, Sylow
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	1	no	—
641	C₂	—	4	1	no	—
642	C₂	C₂²×C₃×#41	1	1	yes	characteristic
643	C₂	C₃×#585	1	1	yes	characteristic
644	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×#556	C₂	semidirect
2. C₃×#556	C₂	semidirect
3. C₃×#554	C₂	semidirect
4. C₃×#553	C₂	semidirect
5. C₃×#553	C₂	semidirect
6. C₃×#552	C₂	semidirect
7. C₃×#552	C₂	semidirect
8. C₃×#551	C₂	semidirect
9. C₃×#551	C₂	semidirect
10. C₃×#547	C₂	semidirect
11. C₃×#546	C₂	semidirect
12. C₃×#546	C₂	semidirect
13. C₃×#542	C₂	semidirect
14. C₃×#541	C₂	semidirect
15. C₃×#539	C₂	semidirect
16. C₃×#538	C₂	semidirect
17. C₃×#529	C₂	semidirect
18. C₃×#529	C₂	semidirect
19. C₃×#529	C₂	semidirect
20. C₂×C₃×#126	C₂	semidirect
21. C₃×#520	C₂	semidirect
22. C₃×#518	C₂	semidirect
23. C₃×C₄×#41	C₂	semidirect
24. #3521	C₃	direct (N × H)
28. C₃×C₄⋊Q₈	C₂²	semidirect
29. C₃×C₄⋊Q₈	C₂²	semidirect
35. C₃×#126	C₂²	semidirect
36. C₃×#126	C₂²	semidirect
37. C₃×#126	C₂²	semidirect
38. C₃×#126	C₂²	semidirect
39. C₃×#126	C₂²	semidirect
40. C₃×#126	C₂²	semidirect
41. C₃×#126	C₂²	semidirect
42. C₃×#125	C₂²	semidirect
43. C₃×#125	C₂²	semidirect
44. C₃×#125	C₂²	semidirect
45. C₃×#125	C₂²	semidirect
46. C₃×#125	C₂²	semidirect
47. C₃×#125	C₂²	semidirect
52. C₃×#124	C₂²	semidirect
57. C₃×#123	C₂²	semidirect
58. C₃×#123	C₂²	semidirect
59. C₃×#123	C₂²	semidirect
60. C₃×#123	C₂²	semidirect
61. C₃×#123	C₂²	semidirect
62. C₃×#123	C₂²	semidirect
65. C₃×C₂²⋊Q₈	C₂²	semidirect
66. C₃×C₂²⋊Q₈	C₂²	semidirect
67. C₃×C₂²⋊Q₈	C₂²	semidirect
68. C₃×C₂²⋊Q₈	C₂²	semidirect
69. C₃×C₂²⋊Q₈	C₂²	semidirect
70. C₃×C₂²⋊Q₈	C₂²	semidirect
71. C₃×C₂²⋊Q₈	C₂²	semidirect
72. C₃×C₂²⋊Q₈	C₂²	semidirect
78. C₃×#121	C₂²	semidirect
79. C₃×#121	C₂²	semidirect
82. C₃×C₄×Q₈	C₂²	semidirect
83. C₃×C₄×Q₈	C₂²	semidirect
84. C₃×C₄×Q₈	C₂²	semidirect
85. C₃×C₄×Q₈	C₂²	semidirect
86. C₃×C₄×Q₈	C₂²	semidirect
87. C₃×C₄×Q₈	C₂²	semidirect
98. C₃×C₄×D₄	C₂²	semidirect
99. C₃×C₄×D₄	C₂²	semidirect
100. C₃×C₄×D₄	C₂²	semidirect
101. C₃×C₄×D₄	C₂²	semidirect
102. C₃×C₄×D₄	C₂²	semidirect
103. C₃×C₄×D₄	C₂²	semidirect
104. C₃×C₄×D₄	C₂²	semidirect
107. C₃×#117	C₂²	semidirect
108. C₃×#117	C₂²	semidirect
109. C₃×#117	C₂²	semidirect
110. C₃×#117	C₂²	semidirect
111. C₃×#117	C₂²	semidirect
112. C₃×#117	C₂²	semidirect
113. C₃×#117	C₂²	semidirect
114. C₂×C₃×C₄⋊C₄	C₂²	semidirect
115. C₂×C₃×C₄⋊C₄	C₂²	semidirect
116. C₂×C₃×C₄⋊C₄	C₂²	semidirect
117. C₂×C₃×C₄⋊C₄	C₂²	semidirect
122. C₂×C₃×C₄²	C₂²	semidirect
123. C₂×C₃×C₄²	C₂²	semidirect
124. #556	C₂×C₃	semidirect
125. #556	C₂×C₃	semidirect
126. #554	C₂×C₃	semidirect
127. #553	C₂×C₃	semidirect
128. #553	C₂×C₃	semidirect
129. #552	C₂×C₃	semidirect
130. #552	C₂×C₃	semidirect
131. #551	C₂×C₃	semidirect
132. #551	C₂×C₃	semidirect
133. #547	C₂×C₃	semidirect
134. #546	C₂×C₃	semidirect
135. #546	C₂×C₃	semidirect
136. #542	C₂×C₃	semidirect
137. #541	C₂×C₃	semidirect
138. #539	C₂×C₃	semidirect
139. #538	C₂×C₃	semidirect
140. #529	C₂×C₃	semidirect
141. #529	C₂×C₃	semidirect
142. #529	C₂×C₃	semidirect
143. C₂×#126	C₂×C₃	semidirect
144. #520	C₂×C₃	semidirect
145. #518	C₂×C₃	semidirect
146. C₄×#41	C₂×C₃	semidirect
252. C₄⋊Q₈	C₂²×C₃	semidirect
253. C₄⋊Q₈	C₂²×C₃	semidirect
259. #126	C₂²×C₃	semidirect
260. #126	C₂²×C₃	semidirect
261. #126	C₂²×C₃	semidirect
262. #126	C₂²×C₃	semidirect
263. #126	C₂²×C₃	semidirect
264. #126	C₂²×C₃	semidirect
265. #126	C₂²×C₃	semidirect
266. #125	C₂²×C₃	semidirect
267. #125	C₂²×C₃	semidirect
268. #125	C₂²×C₃	semidirect
269. #125	C₂²×C₃	semidirect
270. #125	C₂²×C₃	semidirect
271. #125	C₂²×C₃	semidirect
276. #124	C₂²×C₃	semidirect
281. #123	C₂²×C₃	semidirect
282. #123	C₂²×C₃	semidirect
283. #123	C₂²×C₃	semidirect
284. #123	C₂²×C₃	semidirect
285. #123	C₂²×C₃	semidirect
286. #123	C₂²×C₃	semidirect
289. C₂²⋊Q₈	C₂²×C₃	semidirect
290. C₂²⋊Q₈	C₂²×C₃	semidirect
291. C₂²⋊Q₈	C₂²×C₃	semidirect
292. C₂²⋊Q₈	C₂²×C₃	semidirect
293. C₂²⋊Q₈	C₂²×C₃	semidirect
294. C₂²⋊Q₈	C₂²×C₃	semidirect
295. C₂²⋊Q₈	C₂²×C₃	semidirect
296. C₂²⋊Q₈	C₂²×C₃	semidirect
302. #121	C₂²×C₃	semidirect
303. #121	C₂²×C₃	semidirect
306. C₄×Q₈	C₂²×C₃	semidirect
307. C₄×Q₈	C₂²×C₃	semidirect
308. C₄×Q₈	C₂²×C₃	semidirect
309. C₄×Q₈	C₂²×C₃	semidirect
310. C₄×Q₈	C₂²×C₃	semidirect
311. C₄×Q₈	C₂²×C₃	semidirect
322. C₄×D₄	C₂²×C₃	semidirect
323. C₄×D₄	C₂²×C₃	semidirect
324. C₄×D₄	C₂²×C₃	semidirect
325. C₄×D₄	C₂²×C₃	semidirect
326. C₄×D₄	C₂²×C₃	semidirect
327. C₄×D₄	C₂²×C₃	semidirect
328. C₄×D₄	C₂²×C₃	semidirect
331. #117	C₂²×C₃	semidirect
332. #117	C₂²×C₃	semidirect
333. #117	C₂²×C₃	semidirect
334. #117	C₂²×C₃	semidirect
335. #117	C₂²×C₃	semidirect
336. #117	C₂²×C₃	semidirect
337. #117	C₂²×C₃	semidirect
338. C₂×C₄⋊C₄	C₂²×C₃	semidirect
339. C₂×C₄⋊C₄	C₂²×C₃	semidirect
340. C₂×C₄⋊C₄	C₂²×C₃	semidirect
341. C₂×C₄⋊C₄	C₂²×C₃	semidirect
346. C₂×C₄²	C₂²×C₃	semidirect
347. C₂×C₄²	C₂²×C₃	semidirect
636. C₃	#3521	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×#556	2
C₃×#554	2
C₃×#553	2
C₃×#552	2
C₃×#551	2
C₃×#547	2
C₃×#546	2
C₃×#542	2
C₃×#541	2
C₃×#539	2
C₃×#538	2
C₃×#529	2
C₂×C₃×#126	2
C₃×#520	2
C₃×#518	2
C₃×C₄×#41	2
#3521	3

Subgroups — C3×#3521 #87405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3521 #87405