Subgroups — C₂×C₃×#5605 #11900931

Order 1152.

4181 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₂×C₃²×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#939	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#937	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5605	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₃×#894	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#883	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#882	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#534	—	3	1	no	maximal
12	C₂×#5605	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
15	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
16	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×#67	C₂²	1	2	yes	—
19	C₂²×C₃×#67	C₂²	1	2	yes	complemented
20	C₂²×C₃×#67	C₂²	1	2	yes	complemented
21	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×D₃×D₄	—	2	16	no	—
23	C₂×C₃×D₃×D₄	C₂²	1	16	yes	complemented
24	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
25	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
27	C₃²×#121	C₂²	1	8	yes	complemented
28	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
30	C₂×C₃×#217	C₂²	1	2	yes	complemented
31	C₃×#939	C₂²	1	16	yes	complemented
32	C₃×#937	C₂²	1	16	yes	complemented
33	C₃×#930	C₂²	1	8	yes	complemented
34	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
38	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
39	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
41	C₃×#894	C₂²	1	16	yes	complemented
42	C₃×#883	C₂²	1	16	yes	complemented
43	C₃×#882	C₂²	1	16	yes	complemented
44	C₂³×C₃×D₄	—	3	2	no	—
45	C₂²×D₃×D₄	C₂×C₃	1	2	yes	complemented
46	C₃×#534	—	3	16	no	—
47	C₂×C₃×#123	—	3	2	no	—
48	C₂×C₃×#123	—	3	2	no	—
49	C₂×C₃×#121	—	2	1	no	—
50	C₂×C₃×#121	—	3	2	no	—
51	C₂×C₃×#121	—	3	1	no	—
52	C₂×C₃×#121	D₃	1	1	yes	characteristic, complemented
53	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×#120	—	3	2	no	—
55	C₂×C₃×#120	—	3	2	no	—
56	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
57	C₂×#939	C₂×C₃	1	2	yes	complemented
58	C₂×#937	C₂×C₃	1	2	yes	complemented
59	C₂×#930	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
61	#5605	C₂×C₃	1	16	yes	direct product factor
62	C₂×#894	C₂×C₃	1	2	yes	complemented
63	C₂×#883	C₂×C₃	1	2	yes	complemented
64	C₂×#882	C₂×C₃	1	2	yes	complemented
65	C₂⁴×C₃²	C₂³	1	2	yes	—
66	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
67	C₂³×C₃×D₃	—	2	8	no	—
68	C₂³×C₃×D₃	—	4	2	no	—
69	C₂³×C₃×D₃	—	4	2	no	—
70	C₂³×C₃×D₃	—	4	4	no	—
71	C₂³×C₃×D₃	—	4	4	no	—
72	C₂³×C₃×D₃	D₄	1	8	yes	complemented
73	C₂³×C₃×D₃	C₂³	1	2	yes	—
74	C₂³×C₃×D₃	C₂³	1	2	yes	—
75	C₂³×C₃×D₃	C₂³	1	4	yes	—
76	C₂³×C₃×D₃	C₂³	1	8	yes	complemented
77	C₂×C₃²×D₄	—	2	8	no	—
78	C₂×C₃²×D₄	—	4	2	no	—
79	C₂×C₃²×D₄	C₂³	1	8	yes	complemented
80	C₂×C₃²×D₄	C₂³	1	4	yes	complemented
81	C₂²×C₃²×C₄	—	4	2	no	—
82	C₂²×C₃²×C₄	C₂³	1	2	yes	—
83	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
84	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
85	C₂²×C₃²×C₄	C₂³	1	4	yes	complemented
86	C₂×C₃×#67	—	2	8	no	—
87	C₂×C₃×#67	—	2	8	no	—
88	C₂×C₃×#67	—	4	4	no	—
89	C₂×C₃×#67	C₂³	1	8	yes	—
90	C₂×C₃×#67	C₂³	1	8	yes	complemented
91	C₂×C₃×#67	C₂³	1	8	yes	complemented
92	C₂²×C₃×Dic₃	—	4	2	no	—
93	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
94	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
95	C₂²×C₃×Dic₃	C₂³	1	4	yes	complemented
96	C₃×D₃×D₄	—	2	64	no	—
97	C₂×C₃×D₁₂	—	2	8	no	—
98	C₂×C₃×D₁₂	—	4	2	no	—
99	C₂×C₃×D₁₂	C₂³	1	8	yes	—
100	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
101	C₂×C₃×C₄×D₃	—	2	8	no	—
102	C₂×C₃×C₄×D₃	C₂³	1	8	yes	complemented
103	C₃²×C₄⋊C₄	C₂³	1	4	yes	complemented
104	C₃²×C₂²⋊C₄	C₂³	1	8	yes	complemented
105	C₃×#217	C₂³	1	8	yes	complemented
106	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
107	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
108	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
109	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
110	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
111	C₃×Dic₃⋊C₄	C₂³	1	8	yes	complemented
112	C₂×#534	—	3	1	no	Sylow
113	C₂⁵×C₃	—	3	1	no	—
114	C₂⁵×C₃	—	3	2	no	—
115	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
116	C₂⁴×D₃	C₂²×C₃	1	2	yes	complemented
117	C₂²×C₃×D₄	—	2	2	no	—
118	C₂²×C₃×D₄	—	2	1	no	—
119	C₂²×C₃×D₄	—	3	2	no	—
120	C₂²×C₃×D₄	—	3	2	no	—
121	C₂²×C₃×D₄	—	3	2	no	—
122	C₂²×C₃×D₄	—	3	16	no	—
123	C₂²×C₃×D₄	—	3	2	no	—
124	C₂²×C₃×D₄	—	3	1	no	—
125	C₂²×C₃×D₄	—	6	16	no	—
126	C₂²×C₃×D₄	C₂×D₃	1	2	yes	complemented
127	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic, complemented
128	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	complemented
129	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₂³×C₃×C₄	—	2	1	no	—
131	C₂³×C₃×C₄	—	3	1	no	—
132	C₂³×C₃×C₄	—	3	2	no	—
133	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
134	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₂²×#67	C₂²×C₃	1	2	yes	—
136	C₂²×#67	C₂²×C₃	1	2	yes	complemented
137	C₂²×#67	C₂²×C₃	1	2	yes	complemented
138	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₂×D₃×D₄	—	2	16	no	—
140	C₂×D₃×D₄	C₂²×C₃	1	16	yes	complemented
141	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
142	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
143	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
144	C₃×#123	—	3	16	no	—
145	C₃×#123	—	3	16	no	—
146	C₃×#121	—	2	8	no	—
147	C₃×#121	—	3	16	no	—
148	C₃×#121	—	3	8	no	—
149	C₃×#121	C₂×D₃	1	8	yes	complemented
150	C₃×#121	C₂²×C₃	1	8	yes	complemented
151	C₃×#120	—	3	16	no	—
152	C₃×#120	—	3	16	no	—
153	C₂×C₃×C₄⋊C₄	—	2	1	no	—
154	C₂×C₃×C₄⋊C₄	—	3	2	no	—
155	C₂×C₃×C₄⋊C₄	—	3	1	no	—
156	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
157	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
159	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
160	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
161	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
162	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
163	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
164	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
165	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
166	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
167	C₂×#217	C₂²×C₃	1	2	yes	complemented
168	#939	C₂²×C₃	1	16	yes	complemented
169	#937	C₂²×C₃	1	16	yes	complemented
170	#930	C₂²×C₃	1	8	yes	complemented
171	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
172	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
173	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
174	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
175	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
176	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
178	#894	C₂²×C₃	1	16	yes	complemented
179	#883	C₂²×C₃	1	16	yes	complemented
180	#882	C₂²×C₃	1	16	yes	complemented
181	C₂³×C₃²	—	2	2	no	—
182	C₂³×C₃²	—	2	2	no	—
183	C₂³×C₃²	—	2	4	no	—
184	C₂³×C₃²	—	2	4	no	—
185	C₂³×C₃²	—	2	4	no	—
186	C₂³×C₃²	C₂×D₄	1	4	yes	—
187	C₂³×C₃²	C₂⁴	1	4	yes	—
188	C₂³×C₃²	C₂⁴	1	2	yes	—
189	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
190	C₂²×C₃×D₃	—	2	4	no	—
191	C₂²×C₃×D₃	—	2	4	no	—
192	C₂²×C₃×D₃	—	2	4	no	—
193	C₂²×C₃×D₃	—	2	4	no	—
194	C₂²×C₃×D₃	—	2	4	no	—
195	C₂²×C₃×D₃	—	2	16	no	—
196	C₂²×C₃×D₃	—	4	16	no	—
197	C₂²×C₃×D₃	—	4	4	no	—
198	C₂²×C₃×D₃	—	4	4	no	—
199	C₂²×C₃×D₃	—	4	8	no	—
200	C₂²×C₃×D₃	—	4	8	no	—
201	C₂²×C₃×D₃	—	4	32	no	—
202	C₂²×C₃×D₃	C₂×D₄	1	8	yes	—
203	C₂²×C₃×D₃	C₂×D₄	1	16	yes	complemented
204	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
205	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
206	C₃²×D₄	—	2	16	no	—
207	C₃²×D₄	—	4	4	no	—
208	C₂×C₃²×C₄	—	2	2	no	—
209	C₂×C₃²×C₄	—	2	4	no	—
210	C₂×C₃²×C₄	—	2	2	no	—
211	C₂×C₃²×C₄	—	4	4	no	—
212	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
213	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
214	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
215	C₃×#67	—	2	16	no	—
216	C₃×#67	—	2	16	no	—
217	C₃×#67	—	4	8	no	—
218	C₂×C₃×Dic₃	—	2	4	no	—
219	C₂×C₃×Dic₃	—	2	4	no	—
220	C₂×C₃×Dic₃	—	4	4	no	—
221	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
222	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
223	C₃×D₁₂	—	2	16	no	—
224	C₃×D₁₂	—	4	4	no	—
225	C₃×C₄×D₃	—	2	16	no	—
226	C₂³×D₄	—	3	2	no	—
227	#534	—	3	16	no	—
228	C₂×#123	—	3	2	no	—
229	C₂×#123	—	3	2	no	—
230	C₂×#121	—	3	2	no	—
231	C₂×#121	—	3	1	no	—
232	C₂×#121	C₃×D₃	1	1	yes	characteristic, complemented
233	C₂×#120	—	3	2	no	—
234	C₂×#120	—	3	2	no	—
235	C₂²×C₂²⋊C₄	—	3	1	no	—
236	C₂⁴×C₃	—	2	1	no	—
237	C₂⁴×C₃	—	2	2	no	—
238	C₂⁴×C₃	—	3	2	no	—
239	C₂⁴×C₃	—	3	8	no	—
240	C₂⁴×C₃	—	3	4	no	—
241	C₂⁴×C₃	—	3	2	no	—
242	C₂⁴×C₃	—	3	8	no	—
243	C₂⁴×C₃	—	6	8	no	—
244	C₂⁴×C₃	—	12	2	no	—
245	C₂⁴×C₃	—	12	2	no	—
246	C₂⁴×C₃	—	12	4	no	—
247	C₂⁴×C₃	—	12	4	no	—
248	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
249	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
250	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
251	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
252	C₂³×D₃	—	2	8	no	—
253	C₂³×D₃	—	4	2	no	—
254	C₂³×D₃	—	4	2	no	—
255	C₂³×D₃	—	4	4	no	—
256	C₂³×D₃	—	4	4	no	—
257	C₂³×D₃	C₃×D₄	1	8	yes	complemented
258	C₂³×D₃	C₂³×C₃	1	2	yes	—
259	C₂³×D₃	C₂³×C₃	1	2	yes	—
260	C₂³×D₃	C₂³×C₃	1	4	yes	—
261	C₂³×D₃	C₂³×C₃	1	8	yes	complemented
262	C₂×C₃×D₄	—	2	8	no	—
263	C₂×C₃×D₄	—	2	8	no	—
264	C₂×C₃×D₄	—	2	8	no	—
265	C₂×C₃×D₄	—	2	4	no	—
266	C₂×C₃×D₄	—	3	8	no	—
267	C₂×C₃×D₄	—	3	8	no	—
268	C₂×C₃×D₄	—	3	8	no	—
269	C₂×C₃×D₄	—	3	8	no	—
270	C₂×C₃×D₄	—	3	4	no	—
271	C₂×C₃×D₄	—	4	8	no	—
272	C₂×C₃×D₄	—	4	2	no	—
273	C₂×C₃×D₄	—	4	2	no	—
274	C₂×C₃×D₄	—	4	4	no	—
275	C₂×C₃×D₄	—	6	8	no	—
276	C₂×C₃×D₄	—	6	64	no	—
277	C₂×C₃×D₄	—	6	8	no	—
278	C₂×C₃×D₄	—	6	8	no	—
279	C₂×C₃×D₄	—	12	2	no	—
280	C₂×C₃×D₄	—	12	4	no	—
281	C₂×C₃×D₄	C₂²×D₃	1	8	yes	complemented
282	C₂×C₃×D₄	C₂²×D₃	1	4	yes	complemented
283	C₂×C₃×D₄	C₂³×C₃	1	8	yes	complemented
284	C₂×C₃×D₄	C₂³×C₃	1	4	yes	complemented
285	C₂²×C₃×C₄	—	2	1	no	—
286	C₂²×C₃×C₄	—	2	1	no	—
287	C₂²×C₃×C₄	—	2	2	no	—
288	C₂²×C₃×C₄	—	2	4	no	—
289	C₂²×C₃×C₄	—	3	2	no	—
290	C₂²×C₃×C₄	—	3	2	no	—
291	C₂²×C₃×C₄	—	3	4	no	—
292	C₂²×C₃×C₄	—	3	8	no	—
293	C₂²×C₃×C₄	—	4	2	no	—
294	C₂²×C₃×C₄	—	4	2	no	—
295	C₂²×C₃×C₄	—	4	4	no	—
296	C₂²×C₃×C₄	—	6	8	no	—
297	C₂²×C₃×C₄	—	12	2	no	—
298	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
299	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
300	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
301	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	complemented
302	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
303	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
304	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	complemented
306	C₂×#67	—	2	8	no	—
307	C₂×#67	—	2	8	no	—
308	C₂×#67	—	4	4	no	—
309	C₂×#67	C₂³×C₃	1	8	yes	—
310	C₂×#67	C₂³×C₃	1	8	yes	complemented
311	C₂×#67	C₂³×C₃	1	8	yes	complemented
312	C₂²×Dic₃	—	4	2	no	—
313	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
314	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
315	C₂²×Dic₃	C₂³×C₃	1	4	yes	complemented
316	D₃×D₄	—	2	64	no	—
317	C₂×D₁₂	—	2	8	no	—
318	C₂×D₁₂	—	4	2	no	—
319	C₂×D₁₂	C₂³×C₃	1	8	yes	—
320	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
321	C₂×C₄×D₃	—	2	8	no	—
322	C₂×C₄×D₃	C₂³×C₃	1	8	yes	complemented
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	3	8	no	—
325	C₃×C₄⋊C₄	—	3	4	no	—
326	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
327	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
328	C₃×C₂²⋊C₄	—	2	8	no	—
329	C₃×C₂²⋊C₄	—	3	8	no	—
330	C₃×C₂²⋊C₄	—	3	8	no	—
331	C₃×C₂²⋊C₄	—	3	8	no	—
332	C₃×C₂²⋊C₄	—	3	8	no	—
333	C₃×C₂²⋊C₄	—	3	8	no	—
334	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
335	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
336	#217	C₂³×C₃	1	8	yes	complemented
337	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
338	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
339	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
340	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
341	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
342	Dic₃⋊C₄	C₂³×C₃	1	8	yes	complemented
343	C₂²×C₃²	—	2	8	no	—
344	C₂²×C₃²	—	2	2	no	—
345	C₂²×C₃²	—	2	2	no	—
346	C₂²×C₃²	—	2	4	no	—
347	C₂²×C₃²	—	2	4	no	—
348	C₂²×C₃²	—	2	4	no	—
349	C₂²×C₃²	—	4	8	no	—
350	C₂²×C₃²	C₂²×D₄	1	4	yes	—
351	C₂²×C₃²	C₂²×D₄	1	2	yes	—
352	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
353	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
354	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
355	C₂×C₃×D₃	—	2	16	no	—
356	C₂×C₃×D₃	—	2	4	no	—
357	C₂×C₃×D₃	—	2	4	no	—
358	C₂×C₃×D₃	—	2	4	no	—
359	C₂×C₃×D₃	—	2	4	no	—
360	C₂×C₃×D₃	—	2	4	no	—
361	C₂×C₃×D₃	—	4	16	no	—
362	C₂×C₃×D₃	—	4	32	no	—
363	C₂×C₃×D₃	—	4	8	no	—
364	C₂×C₃×D₃	C₂²×D₄	1	8	yes	—
365	C₃²×C₄	—	2	2	no	—
366	C₃²×C₄	—	2	4	no	—
367	C₃²×C₄	—	2	2	no	—
368	C₃×Dic₃	—	2	4	no	—
369	C₃×Dic₃	—	2	4	no	—
370	C₂⁵	—	3	1	no	—
371	C₂⁵	—	3	2	no	—
372	C₂²×D₄	—	3	2	no	—
373	C₂²×D₄	—	3	2	no	—
374	C₂²×D₄	—	3	2	no	—
375	C₂²×D₄	—	3	16	no	—
376	C₂²×D₄	—	3	2	no	—
377	C₂²×D₄	—	3	1	no	—
378	C₂²×D₄	—	6	16	no	—
379	C₂²×D₄	C₂×C₃×D₃	1	2	yes	complemented
380	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
381	C₂³×C₄	—	3	1	no	—
382	C₂³×C₄	—	3	2	no	—
383	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
384	#123	—	3	16	no	—
385	#123	—	3	16	no	—
386	#121	—	3	16	no	—
387	#121	—	3	8	no	—
388	#121	C₂×C₃×D₃	1	8	yes	complemented
389	#120	—	3	16	no	—
390	#120	—	3	16	no	—
391	C₂×C₄⋊C₄	—	3	2	no	—
392	C₂×C₄⋊C₄	—	3	1	no	—
393	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
394	C₂×C₂²⋊C₄	—	3	2	no	—
395	C₂×C₂²⋊C₄	—	3	2	no	—
396	C₂×C₂²⋊C₄	—	3	2	no	—
397	C₂×C₂²⋊C₄	—	3	2	no	—
398	C₂×C₂²⋊C₄	—	3	2	no	—
399	C₂×C₂²⋊C₄	—	3	8	no	—
400	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
401	C₂³×C₃	—	2	2	no	—
402	C₂³×C₃	—	2	2	no	—
403	C₂³×C₃	—	2	2	no	—
404	C₂³×C₃	—	2	2	no	—
405	C₂³×C₃	—	2	4	no	—
406	C₂³×C₃	—	2	4	no	—
407	C₂³×C₃	—	2	4	no	—
408	C₂³×C₃	—	2	4	no	—
409	C₂³×C₃	—	2	4	no	—
410	C₂³×C₃	—	2	4	no	—
411	C₂³×C₃	—	2	1	no	—
412	C₂³×C₃	—	2	2	no	—
413	C₂³×C₃	—	2	4	no	—
414	C₂³×C₃	—	2	4	no	—
415	C₂³×C₃	—	3	8	no	—
416	C₂³×C₃	—	3	4	no	—
417	C₂³×C₃	—	3	16	no	—
418	C₂³×C₃	—	3	4	no	—
419	C₂³×C₃	—	4	2	no	—
420	C₂³×C₃	—	4	2	no	—
421	C₂³×C₃	—	4	4	no	—
422	C₂³×C₃	—	4	4	no	—
423	C₂³×C₃	—	4	4	no	—
424	C₂³×C₃	—	6	16	no	—
425	C₂³×C₃	—	6	4	no	—
426	C₂³×C₃	—	6	4	no	—
427	C₂³×C₃	—	6	4	no	—
428	C₂³×C₃	—	6	4	no	—
429	C₂³×C₃	—	6	4	no	—
430	C₂³×C₃	—	12	4	no	—
431	C₂³×C₃	—	12	4	no	—
432	C₂³×C₃	—	12	16	no	—
433	C₂³×C₃	—	12	8	no	—
434	C₂³×C₃	—	12	8	no	—
435	C₂³×C₃	—	12	32	no	—
436	C₂³×C₃	D₃×D₄	1	4	yes	—
437	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
438	C₂³×C₃	C₂³×D₃	1	4	yes	—
439	C₂³×C₃	C₂³×D₃	1	2	yes	—
440	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
441	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
442	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
443	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
444	C₂²×D₃	—	2	4	no	—
445	C₂²×D₃	—	2	4	no	—
446	C₂²×D₃	—	2	4	no	—
447	C₂²×D₃	—	2	4	no	—
448	C₂²×D₃	—	2	4	no	—
449	C₂²×D₃	—	2	16	no	—
450	C₂²×D₃	—	4	16	no	—
451	C₂²×D₃	—	4	4	no	—
452	C₂²×D₃	—	4	4	no	—
453	C₂²×D₃	—	4	8	no	—
454	C₂²×D₃	—	4	8	no	—
455	C₂²×D₃	—	4	32	no	—
456	C₂²×D₃	C₂×C₃×D₄	1	8	yes	—
457	C₂²×D₃	C₂×C₃×D₄	1	16	yes	complemented
458	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
459	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
460	C₃×D₄	—	2	16	no	—
461	C₃×D₄	—	2	16	no	—
462	C₃×D₄	—	4	16	no	—
463	C₃×D₄	—	4	4	no	—
464	C₃×D₄	—	4	4	no	—
465	C₃×D₄	—	4	8	no	—
466	C₃×D₄	—	6	16	no	—
467	C₃×D₄	—	6	16	no	—
468	C₃×D₄	—	6	16	no	—
469	C₃×D₄	—	12	4	no	—
470	C₃×D₄	—	12	8	no	—
471	C₂×C₃×C₄	—	2	4	no	—
472	C₂×C₃×C₄	—	2	4	no	—
473	C₂×C₃×C₄	—	2	2	no	—
474	C₂×C₃×C₄	—	2	2	no	—
475	C₂×C₃×C₄	—	2	4	no	—
476	C₂×C₃×C₄	—	2	2	no	—
477	C₂×C₃×C₄	—	2	2	no	—
478	C₂×C₃×C₄	—	2	2	no	—
479	C₂×C₃×C₄	—	2	2	no	—
480	C₂×C₃×C₄	—	2	4	no	—
481	C₂×C₃×C₄	—	3	4	no	—
482	C₂×C₃×C₄	—	3	4	no	—
483	C₂×C₃×C₄	—	4	2	no	—
484	C₂×C₃×C₄	—	4	4	no	—
485	C₂×C₃×C₄	—	4	4	no	—
486	C₂×C₃×C₄	—	4	4	no	—
487	C₂×C₃×C₄	—	4	8	no	—
488	C₂×C₃×C₄	—	6	16	no	—
489	C₂×C₃×C₄	—	6	4	no	—
490	C₂×C₃×C₄	—	6	4	no	—
491	C₂×C₃×C₄	—	12	4	no	—
492	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
493	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
494	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
495	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
496	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
497	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
498	#67	—	2	16	no	—
499	#67	—	2	16	no	—
500	#67	—	4	8	no	—
501	C₂×Dic₃	—	2	4	no	—
502	C₂×Dic₃	—	2	4	no	—
503	C₂×Dic₃	—	4	4	no	—
504	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
505	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
506	D₁₂	—	2	16	no	—
507	D₁₂	—	4	4	no	—
508	C₄×D₃	—	2	16	no	—
509	C₂×C₃²	—	2	4	no	—
510	C₂×C₃²	—	4	4	no	—
511	C₂×C₃²	#534	1	4	yes	complemented
512	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
513	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
515	C₃×D₃	—	2	8	no	—
516	C₃×D₃	—	4	4	no	—
517	C₂⁴	—	3	2	no	—
518	C₂⁴	—	3	4	no	—
519	C₂⁴	—	3	8	no	—
520	C₂⁴	—	3	2	no	—
521	C₂⁴	—	3	8	no	—
522	C₂⁴	—	6	8	no	—
523	C₂⁴	—	12	2	no	—
524	C₂⁴	—	12	2	no	—
525	C₂⁴	—	12	4	no	—
526	C₂⁴	—	12	4	no	—
527	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
528	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	3	8	no	—
531	C₂×D₄	—	3	8	no	—
532	C₂×D₄	—	3	8	no	—
533	C₂×D₄	—	3	8	no	—
534	C₂×D₄	—	3	4	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	6	8	no	—
537	C₂×D₄	—	6	64	no	—
538	C₂×D₄	—	6	8	no	—
539	C₂×D₄	—	6	8	no	—
540	C₂×D₄	—	12	2	no	—
541	C₂×D₄	—	12	4	no	—
542	C₂×D₄	C₂²×C₃×D₃	1	8	yes	complemented
543	C₂×D₄	C₂²×C₃×D₃	1	4	yes	complemented
544	C₂²×C₄	—	3	2	no	—
545	C₂²×C₄	—	3	2	no	—
546	C₂²×C₄	—	3	4	no	—
547	C₂²×C₄	—	3	8	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	6	8	no	—
550	C₂²×C₄	—	12	2	no	—
551	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
552	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
553	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
554	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	complemented
555	C₄⋊C₄	—	3	8	no	—
556	C₄⋊C₄	—	3	4	no	—
557	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
558	C₂²⋊C₄	—	3	8	no	—
559	C₂²⋊C₄	—	3	8	no	—
560	C₂²⋊C₄	—	3	8	no	—
561	C₂²⋊C₄	—	3	8	no	—
562	C₂²⋊C₄	—	3	8	no	—
563	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
564	C₂²×C₃	—	2	2	no	—
565	C₂²×C₃	—	2	2	no	—
566	C₂²×C₃	—	2	2	no	—
567	C₂²×C₃	—	2	2	no	—
568	C₂²×C₃	—	2	8	no	—
569	C₂²×C₃	—	2	8	no	—
570	C₂²×C₃	—	2	4	no	—
571	C₂²×C₃	—	2	4	no	—
572	C₂²×C₃	—	2	4	no	—
573	C₂²×C₃	—	2	4	no	—
574	C₂²×C₃	—	2	4	no	—
575	C₂²×C₃	—	2	4	no	—
576	C₂²×C₃	—	2	2	no	—
577	C₂²×C₃	—	2	4	no	—
578	C₂²×C₃	—	2	2	no	—
579	C₂²×C₃	—	2	2	no	—
580	C₂²×C₃	—	2	1	no	—
581	C₂²×C₃	—	3	8	no	—
582	C₂²×C₃	—	4	2	no	—
583	C₂²×C₃	—	4	8	no	—
584	C₂²×C₃	—	4	2	no	—
585	C₂²×C₃	—	4	4	no	—
586	C₂²×C₃	—	4	4	no	—
587	C₂²×C₃	—	4	4	no	—
588	C₂²×C₃	—	4	8	no	—
589	C₂²×C₃	—	4	8	no	—
590	C₂²×C₃	—	6	4	no	—
591	C₂²×C₃	—	6	4	no	—
592	C₂²×C₃	—	6	16	no	—
593	C₂²×C₃	—	6	4	no	—
594	C₂²×C₃	—	6	4	no	—
595	C₂²×C₃	—	6	4	no	—
596	C₂²×C₃	—	8	8	no	—
597	C₂²×C₃	—	12	16	no	—
598	C₂²×C₃	—	12	32	no	—
599	C₂²×C₃	—	12	8	no	—
600	C₂²×C₃	C₂×D₃×D₄	1	4	yes	—
601	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
602	C₂²×C₃	#1004	1	2	yes	—
603	C₂²×C₃	#1009	1	2	yes	—
604	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
605	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
606	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
607	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
608	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
609	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
610	C₂×D₃	—	2	4	no	—
611	C₂×D₃	—	2	4	no	—
612	C₂×D₃	—	2	16	no	—
613	C₂×D₃	—	2	4	no	—
614	C₂×D₃	—	2	4	no	—
615	C₂×D₃	—	2	4	no	—
616	C₂×D₃	—	4	16	no	—
617	C₂×D₃	—	4	32	no	—
618	C₂×D₃	—	4	8	no	—
619	C₂×D₃	C₂²×C₃×D₄	1	8	yes	—
620	C₃×C₄	—	2	4	no	—
621	C₃×C₄	—	2	4	no	—
622	C₃×C₄	—	2	2	no	—
623	C₃×C₄	—	2	2	no	—
624	C₃×C₄	—	2	4	no	—
625	C₃×C₄	—	2	2	no	—
626	C₃×C₄	—	2	2	no	—
627	C₃×C₄	—	4	2	no	—
628	C₃×C₄	—	4	4	no	—
629	C₃×C₄	—	6	4	no	—
630	C₃×C₄	—	6	4	no	—
631	Dic₃	—	2	4	no	—
632	Dic₃	—	2	4	no	—
633	C₃²	C₂×#534	1	1	yes	characteristic, complemented, Sylow
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	4	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	3	8	no	—
640	C₂³	—	3	4	no	—
641	C₂³	—	3	16	no	—
642	C₂³	—	3	4	no	—
643	C₂³	—	6	16	no	—
644	C₂³	—	6	4	no	—
645	C₂³	—	6	4	no	—
646	C₂³	—	6	4	no	—
647	C₂³	—	6	4	no	—
648	C₂³	—	6	4	no	—
649	C₂³	—	12	16	no	—
650	C₂³	—	12	4	no	—
651	C₂³	—	12	4	no	—
652	C₂³	—	12	8	no	—
653	C₂³	—	12	8	no	—
654	C₂³	—	12	32	no	—
655	C₂³	C₃×D₃×D₄	1	4	yes	—
656	C₂³	C₂³×C₃×D₃	1	4	yes	—
657	C₂³	C₂³×C₃×D₃	1	2	yes	—
658	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
659	D₄	—	2	16	no	—
660	D₄	—	4	4	no	—
661	D₄	—	6	16	no	—
662	D₄	—	6	16	no	—
663	D₄	—	6	16	no	—
664	D₄	—	12	4	no	—
665	D₄	—	12	8	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	3	4	no	—
670	C₂×C₄	—	3	4	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	6	16	no	—
673	C₂×C₄	—	6	4	no	—
674	C₂×C₄	—	6	4	no	—
675	C₂×C₄	—	12	4	no	—
676	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
677	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
678	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
679	C₂×C₃	—	2	4	no	—
680	C₂×C₃	—	2	4	no	—
681	C₂×C₃	—	2	4	no	—
682	C₂×C₃	—	2	1	no	—
683	C₂×C₃	—	2	1	no	—
684	C₂×C₃	—	2	1	no	—
685	C₂×C₃	—	4	4	no	—
686	C₂×C₃	—	4	4	no	—
687	C₂×C₃	—	4	4	no	—
688	C₂×C₃	—	6	8	no	—
689	C₂×C₃	—	8	4	no	—
690	C₂×C₃	—	12	4	no	—
691	C₂×C₃	#5605	1	4	yes	direct product factor
692	C₂×C₃	C₃×#534	1	4	yes	complemented
693	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
694	C₂×C₃	C₂×#1004	1	1	yes	characteristic
695	C₂×C₃	C₂×#1009	1	1	yes	characteristic
696	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
697	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
699	D₃	—	2	8	no	—
700	D₃	—	4	4	no	—
701	C₂²	—	2	8	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	3	8	no	—
708	C₂²	—	4	8	no	—
709	C₂²	—	6	16	no	—
710	C₂²	—	6	4	no	—
711	C₂²	—	6	4	no	—
712	C₂²	—	6	4	no	—
713	C₂²	—	6	4	no	—
714	C₂²	—	6	4	no	—
715	C₂²	—	12	16	no	—
716	C₂²	—	12	32	no	—
717	C₂²	—	12	8	no	—
718	C₂²	C₂×C₃×D₃×D₄	1	4	yes	—
719	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
720	C₂²	C₃×#1004	1	2	yes	—
721	C₂²	C₃×#1009	1	2	yes	—
722	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
723	C₄	—	2	4	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	6	4	no	—
727	C₄	—	6	4	no	—
728	C₃	—	2	1	no	—
729	C₃	C₂×#5605	1	1	yes	characteristic, direct product factor
730	C₃	C₂×C₃×#534	1	1	yes	characteristic, complemented
731	C₂	—	2	4	no	—
732	C₂	—	4	4	no	—
733	C₂	—	6	8	no	—
734	C₂	—	12	4	no	—
735	C₂	C₃×#5605	1	4	yes	direct product factor
736	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
737	C₂	C₂×C₃×#1004	1	1	yes	characteristic
738	C₂	C₂×C₃×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#121	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#121	D₃
hypocenter	C₃	C₂×C₃×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₃×D₄	C₂	semidirect
2. C₂×C₃²×#121	C₂	semidirect
3. C₂×C₃×#939	C₂	semidirect
4. C₂×C₃×#937	C₂	semidirect
5. C₂×C₃×#930	C₂	semidirect
6. C₂²×C₃×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₃×#5605	C₂	direct (N × H)
8. C₂×C₃×#894	C₂	semidirect
9. C₂×C₃×#883	C₂	semidirect
10. C₂×C₃×#882	C₂	semidirect
12. C₂×#5605	C₃	direct (N × H)
14. C₂⁴×C₃×D₃	C₂²	semidirect
15. C₂²×C₃²×D₄	C₂²	semidirect
16. C₂²×C₃²×D₄	C₂²	semidirect
17. C₂³×C₃²×C₄	C₂²	semidirect
19. C₂²×C₃×#67	C₂²	semidirect
20. C₂²×C₃×#67	C₂²	semidirect
21. C₂³×C₃×Dic₃	C₂²	semidirect
23. C₂×C₃×D₃×D₄	C₂²	semidirect
25. C₂²×C₃×D₁₂	C₂²	semidirect
26. C₂²×C₃×C₄×D₃	C₂²	semidirect
27. C₃²×#121	C₂²	semidirect
28. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
29. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
30. C₂×C₃×#217	C₂²	semidirect
31. C₃×#939	C₂²	semidirect
32. C₃×#937	C₂²	semidirect
33. C₃×#930	C₂²	semidirect
34. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
38. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
39. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
40. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
41. C₃×#894	C₂²	semidirect
42. C₃×#883	C₂²	semidirect
43. C₃×#882	C₂²	semidirect
45. C₂²×D₃×D₄	C₂×C₃	semidirect
52. C₂×C₃×#121	D₃	semidirect
53. C₂×C₃×#121	C₂×C₃	semidirect
57. C₂×#939	C₂×C₃	semidirect
58. C₂×#937	C₂×C₃	semidirect
59. C₂×#930	C₂×C₃	semidirect
60. C₂²×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
61. #5605	C₂×C₃	direct (N × H)
62. C₂×#894	C₂×C₃	semidirect
63. C₂×#883	C₂×C₃	semidirect
64. C₂×#882	C₂×C₃	semidirect
72. C₂³×C₃×D₃	D₄	semidirect
76. C₂³×C₃×D₃	C₂³	semidirect
79. C₂×C₃²×D₄	C₂³	semidirect
80. C₂×C₃²×D₄	C₂³	semidirect
85. C₂²×C₃²×C₄	C₂³	semidirect
90. C₂×C₃×#67	C₂³	semidirect
91. C₂×C₃×#67	C₂³	semidirect
95. C₂²×C₃×Dic₃	C₂³	semidirect
100. C₂×C₃×D₁₂	C₂³	semidirect
102. C₂×C₃×C₄×D₃	C₂³	semidirect
103. C₃²×C₄⋊C₄	C₂³	semidirect
104. C₃²×C₂²⋊C₄	C₂³	semidirect
105. C₃×#217	C₂³	semidirect
106. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
107. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
108. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
109. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
110. C₃×C₄⋊Dic₃	C₂³	semidirect
111. C₃×Dic₃⋊C₄	C₂³	semidirect
116. C₂⁴×D₃	C₂²×C₃	semidirect
126. C₂²×C₃×D₄	C₂×D₃	semidirect
127. C₂²×C₃×D₄	C₂×D₃	semidirect
128. C₂²×C₃×D₄	C₂²×C₃	semidirect
129. C₂²×C₃×D₄	C₂²×C₃	semidirect
133. C₂³×C₃×C₄	C₂×D₃	semidirect
134. C₂³×C₃×C₄	C₂²×C₃	semidirect
136. C₂²×#67	C₂²×C₃	semidirect
137. C₂²×#67	C₂²×C₃	semidirect
138. C₂³×Dic₃	C₂²×C₃	semidirect
140. C₂×D₃×D₄	C₂²×C₃	semidirect
142. C₂²×D₁₂	C₂²×C₃	semidirect
143. C₂²×C₄×D₃	C₂²×C₃	semidirect
149. C₃×#121	C₂×D₃	semidirect
150. C₃×#121	C₂²×C₃	semidirect
156. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
157. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
165. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
166. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
167. C₂×#217	C₂²×C₃	semidirect
168. #939	C₂²×C₃	semidirect
169. #937	C₂²×C₃	semidirect
170. #930	C₂²×C₃	semidirect
171. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
172. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
173. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
174. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
175. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
176. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
177. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
178. #894	C₂²×C₃	semidirect
179. #883	C₂²×C₃	semidirect
180. #882	C₂²×C₃	semidirect
203. C₂²×C₃×D₃	C₂×D₄	semidirect
232. C₂×#121	C₃×D₃	semidirect
257. C₂³×D₃	C₃×D₄	semidirect
261. C₂³×D₃	C₂³×C₃	semidirect
281. C₂×C₃×D₄	C₂²×D₃	semidirect
282. C₂×C₃×D₄	C₂²×D₃	semidirect
283. C₂×C₃×D₄	C₂³×C₃	semidirect
284. C₂×C₃×D₄	C₂³×C₃	semidirect
301. C₂²×C₃×C₄	C₂²×D₃	semidirect
305. C₂²×C₃×C₄	C₂³×C₃	semidirect
310. C₂×#67	C₂³×C₃	semidirect
311. C₂×#67	C₂³×C₃	semidirect
315. C₂²×Dic₃	C₂³×C₃	semidirect
320. C₂×D₁₂	C₂³×C₃	semidirect
322. C₂×C₄×D₃	C₂³×C₃	semidirect
326. C₃×C₄⋊C₄	C₂²×D₃	semidirect
327. C₃×C₄⋊C₄	C₂³×C₃	semidirect
334. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
335. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
336. #217	C₂³×C₃	semidirect
337. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
338. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
339. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
340. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
341. C₄⋊Dic₃	C₂³×C₃	semidirect
342. Dic₃⋊C₄	C₂³×C₃	semidirect
379. C₂²×D₄	C₂×C₃×D₃	semidirect
380. C₂²×D₄	C₂×C₃×D₃	semidirect
383. C₂³×C₄	C₂×C₃×D₃	semidirect
388. #121	C₂×C₃×D₃	semidirect
393. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
400. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
457. C₂²×D₃	C₂×C₃×D₄	semidirect
511. C₂×C₃²	#534	semidirect
542. C₂×D₄	C₂²×C₃×D₃	semidirect
543. C₂×D₄	C₂²×C₃×D₃	semidirect
554. C₂²×C₄	C₂²×C₃×D₃	semidirect
557. C₄⋊C₄	C₂²×C₃×D₃	semidirect
563. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
633. C₃²	C₂×#534	semidirect
691. C₂×C₃	#5605	direct (N × H)
692. C₂×C₃	C₃×#534	semidirect
729. C₃	C₂×#5605	direct (N × H)
730. C₃	C₂×C₃×#534	semidirect
735. C₂	C₃×#5605	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃×D₄	2
C₂×C₃²×#121	2
C₂×C₃×#939	2
C₂×C₃×#937	2
C₂×C₃×#930	2
C₂²×C₃×(C₂×D₃)⋊C₄	2
C₃×#5605	2
C₂×C₃×#894	2
C₂×C₃×#883	2
C₂×C₃×#882	2
C₂×C₃×#534	3
C₂×#5605	3

Subgroups — C2×C3×#5605 #11900931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5605 #11900931