Subgroups — C₃²×D₄×#67 #13179180

Order 1728.

3512 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×#67	C₂	1	2	yes	maximal, complemented
3	C₂×C₃²×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#953	C₂	1	2	yes	maximal, complemented
5	C₃²×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#939	C₂	1	2	yes	maximal, complemented
7	C₃²×#938	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#937	C₂	1	2	yes	maximal, complemented
9	C₃²×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#930	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×C₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×D₄²	—	3	1	no	maximal
13	C₃×D₄×#67	C₃	1	4	yes	maximal, direct product factor
14	C₂⁴×C₃³	C₂²	1	2	yes	complemented
15	C₂³×C₃²×D₃	C₂²	1	2	yes	complemented
16	C₂×C₃³×D₄	—	2	4	no	—
17	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃³×D₄	C₂²	1	2	yes	complemented
19	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃²×#67	—	2	8	no	—
22	C₂×C₃²×#67	C₂²	1	1	yes	characteristic
23	C₂×C₃²×#67	C₂²	1	2	yes	complemented
24	C₂×C₃²×#67	C₂²	1	2	yes	complemented
25	C₂×C₃²×#67	C₂²	1	2	yes	complemented
26	C₂×C₃²×#67	C₂²	1	2	yes	complemented
27	C₂×C₃²×#67	C₂²	1	2	yes	complemented
28	C₂²×C₃²×Dic₃	C₂²	1	2	yes	complemented
29	C₃²×D₃×D₄	—	2	4	no	—
30	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#217	C₂²	1	1	yes	characteristic, complemented
33	C₃²×#217	C₂²	1	2	yes	complemented
34	C₃²×#217	C₂²	1	2	yes	complemented
35	C₃²×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₃²×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₃²×D₄	—	2	4	no	—
41	C₂²×C₃²×D₄	—	3	1	no	—
42	C₂²×C₃²×D₄	—	3	2	no	—
43	C₂²×C₃²×D₄	D₃	1	1	yes	characteristic, complemented
44	C₂²×C₃²×D₄	C₂×C₃	1	4	yes	complemented
45	C₂²×C₃×#67	C₂×C₃	1	8	yes	complemented
46	C₂×C₃×D₃×D₄	C₂×C₃	1	4	yes	complemented
47	C₃²×#127	—	3	1	no	—
48	C₃²×#121	—	3	1	no	—
49	C₃²×#121	—	3	2	no	—
50	C₃²×#121	—	3	1	no	—
51	C₃²×#120	—	3	2	no	—
52	C₃²×#120	—	3	2	no	—
53	C₃²×C₄×D₄	—	3	1	no	—
54	C₃²×C₄×D₄	—	3	1	no	—
55	C₃×#953	C₂×C₃	1	8	yes	complemented
56	C₃×#940	C₂×C₃	1	4	yes	complemented
57	C₃×#939	C₂×C₃	1	8	yes	complemented
58	C₃×#938	C₂×C₃	1	4	yes	complemented
59	C₃×#937	C₂×C₃	1	8	yes	complemented
60	C₃×D₄×Dic₃	C₂×C₃	1	4	yes	complemented
61	C₃×#930	C₂×C₃	1	4	yes	complemented
62	C₃×C₄×#67	C₂×C₃	1	4	yes	complemented
63	C₂³×C₃³	—	2	4	no	—
64	C₂³×C₃³	—	2	4	no	—
65	C₂³×C₃³	—	4	2	no	—
66	C₂³×C₃³	C₂³	1	2	yes	—
67	C₂³×C₃³	C₂³	1	2	yes	—
68	C₂³×C₃³	C₂³	1	1	yes	characteristic
69	C₂²×C₃²×D₃	—	2	4	no	—
70	C₂²×C₃²×D₃	—	2	4	no	—
71	C₂²×C₃²×D₃	—	4	2	no	—
72	C₂²×C₃²×D₃	C₂³	1	2	yes	—
73	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
74	C₃³×D₄	—	2	4	no	—
75	C₃³×D₄	—	2	2	no	—
76	C₃³×D₄	D₄	1	4	yes	complemented
77	C₂×C₃³×C₄	—	2	2	no	—
78	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
79	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
80	C₃²×#67	—	2	4	no	—
81	C₃²×#67	—	2	4	no	—
82	C₃²×#67	—	2	4	no	—
83	C₃²×#67	—	2	4	no	—
84	C₃²×#67	—	4	2	no	—
85	C₃²×#67	D₄	1	4	yes	direct product factor
86	C₂×C₃²×Dic₃	—	2	4	no	—
87	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
88	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
89	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
90	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
91	C₃²×D₁₂	—	2	2	no	—
92	C₃²×C₄×D₃	—	2	2	no	—
93	C₃×D₄²	—	3	4	no	—
94	D₄×#67	C₃²	1	1	yes	characteristic, direct product factor
95	C₂⁴×C₃²	—	2	8	no	—
96	C₂⁴×C₃²	—	3	2	no	—
97	C₂⁴×C₃²	C₂×D₃	1	2	yes	complemented
98	C₂⁴×C₃²	C₂²×C₃	1	8	yes	complemented
99	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	complemented
100	C₂×C₃²×D₄	—	2	32	no	—
101	C₂×C₃²×D₄	—	2	4	no	—
102	C₂×C₃²×D₄	—	2	8	no	—
103	C₂×C₃²×D₄	—	2	4	no	—
104	C₂×C₃²×D₄	—	2	4	no	—
105	C₂×C₃²×D₄	—	2	16	no	—
106	C₂×C₃²×D₄	—	3	1	no	—
107	C₂×C₃²×D₄	—	3	2	no	—
108	C₂×C₃²×D₄	—	3	2	no	—
109	C₂×C₃²×D₄	—	3	2	no	—
110	C₂×C₃²×D₄	—	3	2	no	—
111	C₂×C₃²×D₄	—	3	2	no	—
112	C₂×C₃²×D₄	—	3	1	no	—
113	C₂×C₃²×D₄	—	6	8	no	—
114	C₂×C₃²×D₄	—	6	4	no	—
115	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
116	C₂×C₃²×D₄	C₂×D₃	1	2	yes	complemented
117	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
118	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
119	C₂×C₃²×D₄	C₂²×C₃	1	8	yes	complemented
120	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	complemented
121	C₂²×C₃²×C₄	—	2	4	no	—
122	C₂²×C₃²×C₄	—	3	2	no	—
123	C₂²×C₃²×C₄	—	3	1	no	—
124	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic, complemented
125	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	complemented
126	C₂×C₃×#67	—	2	32	no	—
127	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
128	C₂×C₃×#67	C₂²×C₃	1	8	yes	complemented
129	C₂×C₃×#67	C₂²×C₃	1	8	yes	complemented
130	C₂×C₃×#67	C₂²×C₃	1	8	yes	complemented
131	C₂×C₃×#67	C₂²×C₃	1	8	yes	complemented
132	C₂×C₃×#67	C₂²×C₃	1	8	yes	complemented
133	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	complemented
134	C₃×D₃×D₄	—	2	16	no	—
135	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	complemented
136	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	complemented
137	C₃²×C₄⋊C₄	—	3	1	no	—
138	C₃²×C₄⋊C₄	—	3	1	no	—
139	C₃²×C₂²⋊C₄	—	3	1	no	—
140	C₃²×C₂²⋊C₄	—	3	2	no	—
141	C₃²×C₂²⋊C₄	—	3	2	no	—
142	C₃²×C₂²⋊C₄	—	3	1	no	—
143	C₃²×C₂²⋊C₄	—	3	2	no	—
144	C₃²×C₄²	—	3	1	no	—
145	C₃×#217	C₂²×C₃	1	4	yes	complemented
146	C₃×#217	C₂²×C₃	1	8	yes	complemented
147	C₃×#217	C₂²×C₃	1	8	yes	complemented
148	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	complemented
149	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
150	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	complemented
151	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	complemented
152	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	complemented
153	C₂²×C₃³	—	2	1	no	—
154	C₂²×C₃³	—	2	2	no	—
155	C₂²×C₃³	—	2	1	no	—
156	C₂²×C₃³	—	2	2	no	—
157	C₂²×C₃³	—	2	2	no	—
158	C₂²×C₃³	—	2	2	no	—
159	C₂²×C₃³	—	2	2	no	—
160	C₂²×C₃³	—	4	8	no	—
161	C₂²×C₃³	C₂×D₄	1	2	yes	complemented
162	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
163	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
164	C₂×C₃²×D₃	—	2	1	no	—
165	C₂×C₃²×D₃	—	2	1	no	—
166	C₂×C₃²×D₃	—	2	2	no	—
167	C₂×C₃²×D₃	—	2	2	no	—
168	C₂×C₃²×D₃	—	2	2	no	—
169	C₂×C₃²×D₃	—	4	8	no	—
170	C₂×C₃²×D₃	C₂×D₄	1	2	yes	complemented
171	C₃³×C₄	—	2	1	no	—
172	C₃³×C₄	C₂×D₄	1	2	yes	complemented
173	C₃²×Dic₃	—	2	1	no	—
174	C₃²×Dic₃	—	2	2	no	—
175	C₃²×Dic₃	—	2	1	no	—
176	C₃²×Dic₃	C₂×D₄	1	2	yes	complemented
177	C₂²×C₃×D₄	—	2	4	no	—
178	C₂²×C₃×D₄	—	3	8	no	—
179	C₂²×C₃×D₄	—	3	4	no	—
180	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
181	C₂²×C₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
182	C₂²×#67	C₂×C₃²	1	2	yes	complemented
183	C₂×D₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
184	C₃×#127	—	3	4	no	—
185	C₃×#121	—	3	4	no	—
186	C₃×#121	—	3	8	no	—
187	C₃×#121	—	3	4	no	—
188	C₃×#120	—	3	8	no	—
189	C₃×#120	—	3	8	no	—
190	C₃×C₄×D₄	—	3	4	no	—
191	C₃×C₄×D₄	—	3	4	no	—
192	#953	C₂×C₃²	1	2	yes	complemented
193	#940	C₂×C₃²	1	1	yes	characteristic, complemented
194	#939	C₂×C₃²	1	2	yes	complemented
195	#938	C₂×C₃²	1	1	yes	characteristic, complemented
196	#937	C₂×C₃²	1	2	yes	complemented
197	D₄×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
198	#930	C₂×C₃²	1	1	yes	characteristic, complemented
199	C₄×#67	C₂×C₃²	1	1	yes	characteristic, complemented
200	C₂³×C₃²	—	2	32	no	—
201	C₂³×C₃²	—	2	4	no	—
202	C₂³×C₃²	—	2	4	no	—
203	C₂³×C₃²	—	2	16	no	—
204	C₂³×C₃²	—	2	4	no	—
205	C₂³×C₃²	—	2	8	no	—
206	C₂³×C₃²	—	2	8	no	—
207	C₂³×C₃²	—	2	16	no	—
208	C₂³×C₃²	—	3	1	no	—
209	C₂³×C₃²	—	3	2	no	—
210	C₂³×C₃²	—	4	16	no	—
211	C₂³×C₃²	—	4	2	no	—
212	C₂³×C₃²	—	4	8	no	—
213	C₂³×C₃²	—	4	16	no	—
214	C₂³×C₃²	—	6	4	no	—
215	C₂³×C₃²	—	6	4	no	—
216	C₂³×C₃²	—	12	2	no	—
217	C₂³×C₃²	C₂²×D₃	1	2	yes	—
218	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
219	C₂³×C₃²	C₂²×D₃	1	2	yes	—
220	C₂³×C₃²	C₂³×C₃	1	8	yes	—
221	C₂³×C₃²	C₂³×C₃	1	8	yes	—
222	C₂³×C₃²	C₂³×C₃	1	4	yes	—
223	C₂²×C₃×D₃	—	2	16	no	—
224	C₂²×C₃×D₃	—	2	16	no	—
225	C₂²×C₃×D₃	—	4	8	no	—
226	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
227	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
228	C₃²×D₄	—	2	32	no	—
229	C₃²×D₄	—	2	16	no	—
230	C₃²×D₄	—	2	4	no	—
231	C₃²×D₄	—	2	16	no	—
232	C₃²×D₄	—	2	2	no	—
233	C₃²×D₄	—	2	8	no	—
234	C₃²×D₄	—	2	16	no	—
235	C₃²×D₄	—	3	4	no	—
236	C₃²×D₄	—	6	4	no	—
237	C₃²×D₄	—	6	4	no	—
238	C₃²×D₄	—	6	4	no	—
239	C₃²×D₄	—	6	4	no	—
240	C₃²×D₄	—	6	2	no	—
241	C₃²×D₄	—	12	2	no	—
242	C₃²×D₄	#67	1	4	yes	direct product factor
243	C₃²×D₄	C₃×D₄	1	16	yes	complemented
244	C₂×C₃²×C₄	—	2	16	no	—
245	C₂×C₃²×C₄	—	2	2	no	—
246	C₂×C₃²×C₄	—	2	8	no	—
247	C₂×C₃²×C₄	—	2	4	no	—
248	C₂×C₃²×C₄	—	2	4	no	—
249	C₂×C₃²×C₄	—	3	1	no	—
250	C₂×C₃²×C₄	—	3	1	no	—
251	C₂×C₃²×C₄	—	3	2	no	—
252	C₂×C₃²×C₄	—	3	1	no	—
253	C₂×C₃²×C₄	—	6	4	no	—
254	C₂×C₃²×C₄	—	6	2	no	—
255	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
256	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
257	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
258	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
259	C₃×#67	—	2	16	no	—
260	C₃×#67	—	2	16	no	—
261	C₃×#67	—	2	16	no	—
262	C₃×#67	—	2	16	no	—
263	C₃×#67	—	4	8	no	—
264	C₃×#67	C₃×D₄	1	16	yes	direct product factor
265	C₂×C₃×Dic₃	—	2	16	no	—
266	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
267	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
268	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
269	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
270	C₃×D₁₂	—	2	8	no	—
271	C₃×C₄×D₃	—	2	8	no	—
272	D₄²	—	3	1	no	Sylow
273	C₂×C₃³	—	2	2	no	—
274	C₂×C₃³	—	2	4	no	—
275	C₂×C₃³	—	4	2	no	—
276	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
279	C₃²×D₃	—	2	2	no	—
280	C₃²×D₃	—	4	2	no	—
281	C₂⁴×C₃	—	2	8	no	—
282	C₂⁴×C₃	—	3	8	no	—
283	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	complemented
284	C₂⁴×C₃	C₂²×C₃²	1	2	yes	complemented
285	C₂³×D₃	C₂²×C₃²	1	2	yes	complemented
286	C₂×C₃×D₄	—	2	32	no	—
287	C₂×C₃×D₄	—	2	16	no	—
288	C₂×C₃×D₄	—	2	4	no	—
289	C₂×C₃×D₄	—	2	4	no	—
290	C₂×C₃×D₄	—	2	8	no	—
291	C₂×C₃×D₄	—	2	4	no	—
292	C₂×C₃×D₄	—	3	4	no	—
293	C₂×C₃×D₄	—	3	8	no	—
294	C₂×C₃×D₄	—	3	8	no	—
295	C₂×C₃×D₄	—	3	8	no	—
296	C₂×C₃×D₄	—	3	8	no	—
297	C₂×C₃×D₄	—	3	8	no	—
298	C₂×C₃×D₄	—	3	4	no	—
299	C₂×C₃×D₄	—	6	32	no	—
300	C₂×C₃×D₄	—	6	16	no	—
301	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
302	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	complemented
303	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
304	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
305	C₂×C₃×D₄	C₂²×C₃²	1	2	yes	complemented
306	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
307	C₂²×C₃×C₄	—	2	4	no	—
308	C₂²×C₃×C₄	—	3	8	no	—
309	C₂²×C₃×C₄	—	3	4	no	—
310	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
311	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
312	C₂×#67	—	2	8	no	—
313	C₂×#67	C₂²×C₃²	1	1	yes	characteristic
314	C₂×#67	C₂²×C₃²	1	2	yes	complemented
315	C₂×#67	C₂²×C₃²	1	2	yes	complemented
316	C₂×#67	C₂²×C₃²	1	2	yes	complemented
317	C₂×#67	C₂²×C₃²	1	2	yes	complemented
318	C₂×#67	C₂²×C₃²	1	2	yes	complemented
319	C₂²×Dic₃	C₂²×C₃²	1	2	yes	complemented
320	D₃×D₄	—	2	4	no	—
321	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic, complemented
322	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic, complemented
323	C₃×C₄⋊C₄	—	3	4	no	—
324	C₃×C₄⋊C₄	—	3	4	no	—
325	C₃×C₂²⋊C₄	—	3	4	no	—
326	C₃×C₂²⋊C₄	—	3	8	no	—
327	C₃×C₂²⋊C₄	—	3	8	no	—
328	C₃×C₂²⋊C₄	—	3	4	no	—
329	C₃×C₂²⋊C₄	—	3	8	no	—
330	C₃×C₄²	—	3	4	no	—
331	#217	C₂²×C₃²	1	1	yes	characteristic, complemented
332	#217	C₂²×C₃²	1	2	yes	complemented
333	#217	C₂²×C₃²	1	2	yes	complemented
334	(C₂×D₃)⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
335	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	complemented
336	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
337	Dic₃⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
338	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
339	C₂²×C₃²	—	2	8	no	—
340	C₂²×C₃²	—	2	8	no	—
341	C₂²×C₃²	—	2	2	no	—
342	C₂²×C₃²	—	2	1	no	—
343	C₂²×C₃²	—	2	2	no	—
344	C₂²×C₃²	—	2	1	no	—
345	C₂²×C₃²	—	2	4	no	—
346	C₂²×C₃²	—	2	4	no	—
347	C₂²×C₃²	—	2	16	no	—
348	C₂²×C₃²	—	2	2	no	—
349	C₂²×C₃²	—	2	2	no	—
350	C₂²×C₃²	—	2	2	no	—
351	C₂²×C₃²	—	2	8	no	—
352	C₂²×C₃²	—	2	4	no	—
353	C₂²×C₃²	—	2	8	no	—
354	C₂²×C₃²	—	2	16	no	—
355	C₂²×C₃²	—	2	8	no	—
356	C₂²×C₃²	—	2	8	no	—
357	C₂²×C₃²	—	2	8	no	—
358	C₂²×C₃²	—	2	8	no	—
359	C₂²×C₃²	—	3	2	no	—
360	C₂²×C₃²	—	4	8	no	—
361	C₂²×C₃²	—	4	8	no	—
362	C₂²×C₃²	—	4	8	no	—
363	C₂²×C₃²	—	4	8	no	—
364	C₂²×C₃²	—	4	8	no	—
365	C₂²×C₃²	—	4	32	no	—
366	C₂²×C₃²	—	4	64	no	—
367	C₂²×C₃²	—	6	1	no	—
368	C₂²×C₃²	—	6	1	no	—
369	C₂²×C₃²	—	6	2	no	—
370	C₂²×C₃²	—	6	2	no	—
371	C₂²×C₃²	—	6	2	no	—
372	C₂²×C₃²	—	12	8	no	—
373	C₂²×C₃²	D₃×D₄	1	2	yes	complemented
374	C₂²×C₃²	C₂×#67	1	4	yes	complemented
375	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	complemented
376	C₂²×C₃²	C₂×C₃×D₄	1	16	yes	complemented
377	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
378	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
379	C₂×C₃×D₃	—	2	4	no	—
380	C₂×C₃×D₃	—	2	4	no	—
381	C₂×C₃×D₃	—	2	8	no	—
382	C₂×C₃×D₃	—	2	8	no	—
383	C₂×C₃×D₃	—	2	8	no	—
384	C₂×C₃×D₃	—	4	32	no	—
385	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	complemented
386	C₃²×C₄	—	2	8	no	—
387	C₃²×C₄	—	2	1	no	—
388	C₃²×C₄	—	2	4	no	—
389	C₃²×C₄	—	2	8	no	—
390	C₃²×C₄	—	3	2	no	—
391	C₃²×C₄	—	6	2	no	—
392	C₃²×C₄	—	6	1	no	—
393	C₃²×C₄	—	6	1	no	—
394	C₃²×C₄	C₂×#67	1	2	yes	complemented
395	C₃²×C₄	C₂×C₃×D₄	1	8	yes	complemented
396	C₃×Dic₃	—	2	4	no	—
397	C₃×Dic₃	—	2	8	no	—
398	C₃×Dic₃	—	2	4	no	—
399	C₃×Dic₃	C₂×C₃×D₄	1	8	yes	complemented
400	C₂²×D₄	—	3	2	no	—
401	C₂²×D₄	—	3	1	no	—
402	C₂²×D₄	C₃²×D₃	1	1	yes	characteristic, complemented
403	#127	—	3	1	no	—
404	#121	—	3	1	no	—
405	#121	—	3	2	no	—
406	#121	—	3	1	no	—
407	#120	—	3	2	no	—
408	#120	—	3	2	no	—
409	C₄×D₄	—	3	1	no	—
410	C₄×D₄	—	3	1	no	—
411	C₃³	D₄²	1	1	yes	characteristic, complemented, Sylow
412	C₂³×C₃	—	2	32	no	—
413	C₂³×C₃	—	2	16	no	—
414	C₂³×C₃	—	2	16	no	—
415	C₂³×C₃	—	2	4	no	—
416	C₂³×C₃	—	2	4	no	—
417	C₂³×C₃	—	2	4	no	—
418	C₂³×C₃	—	2	8	no	—
419	C₂³×C₃	—	2	8	no	—
420	C₂³×C₃	—	3	4	no	—
421	C₂³×C₃	—	3	8	no	—
422	C₂³×C₃	—	4	16	no	—
423	C₂³×C₃	—	4	8	no	—
424	C₂³×C₃	—	4	2	no	—
425	C₂³×C₃	—	4	16	no	—
426	C₂³×C₃	—	6	16	no	—
427	C₂³×C₃	—	6	16	no	—
428	C₂³×C₃	—	12	8	no	—
429	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
430	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
431	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
432	C₂³×C₃	C₂³×C₃²	1	2	yes	—
433	C₂³×C₃	C₂³×C₃²	1	2	yes	—
434	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
435	C₂²×D₃	—	2	4	no	—
436	C₂²×D₃	—	2	4	no	—
437	C₂²×D₃	—	4	2	no	—
438	C₂²×D₃	C₂³×C₃²	1	2	yes	—
439	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
440	C₃×D₄	—	2	32	no	—
441	C₃×D₄	—	2	16	no	—
442	C₃×D₄	—	2	16	no	—
443	C₃×D₄	—	2	4	no	—
444	C₃×D₄	—	2	8	no	—
445	C₃×D₄	—	2	2	no	—
446	C₃×D₄	—	2	16	no	—
447	C₃×D₄	—	3	16	no	—
448	C₃×D₄	—	6	16	no	—
449	C₃×D₄	—	6	16	no	—
450	C₃×D₄	—	6	16	no	—
451	C₃×D₄	—	6	16	no	—
452	C₃×D₄	—	6	8	no	—
453	C₃×D₄	—	12	8	no	—
454	C₃×D₄	C₃×#67	1	16	yes	direct product factor
455	C₃×D₄	C₃²×D₄	1	4	yes	complemented
456	C₂×C₃×C₄	—	2	16	no	—
457	C₂×C₃×C₄	—	2	8	no	—
458	C₂×C₃×C₄	—	2	2	no	—
459	C₂×C₃×C₄	—	2	4	no	—
460	C₂×C₃×C₄	—	2	4	no	—
461	C₂×C₃×C₄	—	3	4	no	—
462	C₂×C₃×C₄	—	3	4	no	—
463	C₂×C₃×C₄	—	3	8	no	—
464	C₂×C₃×C₄	—	3	4	no	—
465	C₂×C₃×C₄	—	6	16	no	—
466	C₂×C₃×C₄	—	6	8	no	—
467	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
468	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
469	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
471	#67	—	2	4	no	—
472	#67	—	2	4	no	—
473	#67	—	2	4	no	—
474	#67	—	2	4	no	—
475	#67	—	4	2	no	—
476	#67	C₃²×D₄	1	4	yes	direct product factor
477	C₂×Dic₃	—	2	4	no	—
478	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
479	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
480	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
481	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
482	D₁₂	—	2	2	no	—
483	C₄×D₃	—	2	2	no	—
484	C₂×C₃²	—	2	16	no	—
485	C₂×C₃²	—	2	2	no	—
486	C₂×C₃²	—	2	4	no	—
487	C₂×C₃²	—	2	8	no	—
488	C₂×C₃²	—	2	4	no	—
489	C₂×C₃²	—	2	4	no	—
490	C₂×C₃²	—	2	4	no	—
491	C₂×C₃²	—	2	16	no	—
492	C₂×C₃²	—	4	16	no	—
493	C₂×C₃²	—	4	16	no	—
494	C₂×C₃²	—	4	2	no	—
495	C₂×C₃²	—	4	8	no	—
496	C₂×C₃²	—	6	2	no	—
497	C₂×C₃²	—	12	2	no	—
498	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
499	C₂×C₃²	#1004	1	1	yes	characteristic
500	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
501	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
502	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
503	C₂×C₃²	C₃×H(5,𝔽₂)	1	4	yes	—
504	C₃×D₃	—	2	8	no	—
505	C₃×D₃	—	4	8	no	—
506	C₂⁴	—	3	2	no	—
507	C₂⁴	C₂×C₃²×D₃	1	2	yes	complemented
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	3	1	no	—
510	C₂×D₄	—	3	2	no	—
511	C₂×D₄	—	3	2	no	—
512	C₂×D₄	—	3	2	no	—
513	C₂×D₄	—	3	2	no	—
514	C₂×D₄	—	3	2	no	—
515	C₂×D₄	—	3	1	no	—
516	C₂×D₄	—	6	8	no	—
517	C₂×D₄	—	6	4	no	—
518	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
519	C₂×D₄	C₂×C₃²×D₃	1	2	yes	complemented
520	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
521	C₂²×C₄	—	3	2	no	—
522	C₂²×C₄	—	3	1	no	—
523	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
524	C₄⋊C₄	—	3	1	no	—
525	C₄⋊C₄	—	3	1	no	—
526	C₂²⋊C₄	—	3	1	no	—
527	C₂²⋊C₄	—	3	2	no	—
528	C₂²⋊C₄	—	3	2	no	—
529	C₂²⋊C₄	—	3	1	no	—
530	C₂²⋊C₄	—	3	2	no	—
531	C₄²	—	3	1	no	—
532	C₂²×C₃	—	2	8	no	—
533	C₂²×C₃	—	2	8	no	—
534	C₂²×C₃	—	2	8	no	—
535	C₂²×C₃	—	2	4	no	—
536	C₂²×C₃	—	2	8	no	—
537	C₂²×C₃	—	2	4	no	—
538	C₂²×C₃	—	2	2	no	—
539	C₂²×C₃	—	2	1	no	—
540	C₂²×C₃	—	2	2	no	—
541	C₂²×C₃	—	2	1	no	—
542	C₂²×C₃	—	2	16	no	—
543	C₂²×C₃	—	2	8	no	—
544	C₂²×C₃	—	2	8	no	—
545	C₂²×C₃	—	2	8	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	—	2	2	no	—
549	C₂²×C₃	—	2	4	no	—
550	C₂²×C₃	—	2	8	no	—
551	C₂²×C₃	—	2	16	no	—
552	C₂²×C₃	—	3	8	no	—
553	C₂²×C₃	—	4	8	no	—
554	C₂²×C₃	—	4	8	no	—
555	C₂²×C₃	—	4	8	no	—
556	C₂²×C₃	—	4	8	no	—
557	C₂²×C₃	—	4	32	no	—
558	C₂²×C₃	—	4	8	no	—
559	C₂²×C₃	—	4	64	no	—
560	C₂²×C₃	—	6	4	no	—
561	C₂²×C₃	—	6	4	no	—
562	C₂²×C₃	—	6	8	no	—
563	C₂²×C₃	—	6	8	no	—
564	C₂²×C₃	—	6	8	no	—
565	C₂²×C₃	—	12	32	no	—
566	C₂²×C₃	C₃×D₃×D₄	1	8	yes	complemented
567	C₂²×C₃	C₂×C₃×#67	1	16	yes	complemented
568	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	complemented
569	C₂²×C₃	C₂×C₃²×D₄	1	4	yes	complemented
570	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
571	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
572	C₂×D₃	—	2	1	no	—
573	C₂×D₃	—	2	1	no	—
574	C₂×D₃	—	2	2	no	—
575	C₂×D₃	—	2	2	no	—
576	C₂×D₃	—	2	2	no	—
577	C₂×D₃	—	4	8	no	—
578	C₂×D₃	C₂×C₃²×D₄	1	2	yes	complemented
579	C₃×C₄	—	2	8	no	—
580	C₃×C₄	—	2	4	no	—
581	C₃×C₄	—	2	1	no	—
582	C₃×C₄	—	2	8	no	—
583	C₃×C₄	—	3	8	no	—
584	C₃×C₄	—	6	8	no	—
585	C₃×C₄	—	6	4	no	—
586	C₃×C₄	—	6	4	no	—
587	C₃×C₄	C₂×C₃×#67	1	8	yes	complemented
588	C₃×C₄	C₂×C₃²×D₄	1	2	yes	complemented
589	Dic₃	—	2	1	no	—
590	Dic₃	—	2	2	no	—
591	Dic₃	—	2	1	no	—
592	Dic₃	C₂×C₃²×D₄	1	2	yes	complemented
593	C₃²	—	2	4	no	—
594	C₃²	D₄×#67	1	1	yes	characteristic, direct product factor
595	C₃²	C₃×D₄²	1	4	yes	complemented
596	C₂³	—	2	4	no	—
597	C₂³	—	2	4	no	—
598	C₂³	—	3	1	no	—
599	C₂³	—	3	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	6	4	no	—
602	C₂³	—	6	4	no	—
603	C₂³	—	12	2	no	—
604	C₂³	C₂²×C₃²×D₃	1	2	yes	—
605	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
606	C₂³	C₂²×C₃²×D₃	1	2	yes	—
607	D₄	—	2	4	no	—
608	D₄	—	2	2	no	—
609	D₄	—	3	4	no	—
610	D₄	—	6	4	no	—
611	D₄	—	6	4	no	—
612	D₄	—	6	4	no	—
613	D₄	—	6	4	no	—
614	D₄	—	6	2	no	—
615	D₄	—	12	2	no	—
616	D₄	C₃²×#67	1	4	yes	direct product factor
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	3	1	no	—
619	C₂×C₄	—	3	1	no	—
620	C₂×C₄	—	3	2	no	—
621	C₂×C₄	—	3	1	no	—
622	C₂×C₄	—	6	4	no	—
623	C₂×C₄	—	6	2	no	—
624	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
625	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
626	C₂×C₃	—	2	16	no	—
627	C₂×C₃	—	2	8	no	—
628	C₂×C₃	—	2	16	no	—
629	C₂×C₃	—	2	4	no	—
630	C₂×C₃	—	2	2	no	—
631	C₂×C₃	—	2	4	no	—
632	C₂×C₃	—	2	4	no	—
633	C₂×C₃	—	2	4	no	—
634	C₂×C₃	—	4	16	no	—
635	C₂×C₃	—	4	16	no	—
636	C₂×C₃	—	4	8	no	—
637	C₂×C₃	—	4	2	no	—
638	C₂×C₃	—	6	8	no	—
639	C₂×C₃	—	12	8	no	—
640	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
641	C₂×C₃	C₃×#1004	1	4	yes	—
642	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
643	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
644	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
645	C₂×C₃	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
646	D₃	—	2	2	no	—
647	D₃	—	4	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	3	2	no	—
656	C₂²	—	4	8	no	—
657	C₂²	—	6	1	no	—
658	C₂²	—	6	1	no	—
659	C₂²	—	6	2	no	—
660	C₂²	—	6	2	no	—
661	C₂²	—	6	2	no	—
662	C₂²	—	12	8	no	—
663	C₂²	C₃²×D₃×D₄	1	2	yes	complemented
664	C₂²	C₂×C₃²×#67	1	4	yes	complemented
665	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
666	C₄	—	2	1	no	—
667	C₄	—	3	2	no	—
668	C₄	—	6	2	no	—
669	C₄	—	6	1	no	—
670	C₄	—	6	1	no	—
671	C₄	C₂×C₃²×#67	1	2	yes	complemented
672	C₃	—	2	4	no	—
673	C₃	C₃×D₄×#67	1	4	yes	direct product factor
674	C₃	C₃²×D₄²	1	1	yes	characteristic, complemented
675	C₂	—	2	2	no	—
676	C₂	—	2	4	no	—
677	C₂	—	4	2	no	—
678	C₂	—	6	2	no	—
679	C₂	—	12	2	no	—
680	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic
681	C₂	C₃²×#1004	1	1	yes	characteristic
682	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂²×C₃²×D₄	D₃
hypocenter	C₃	C₃²×D₄²
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×D₄	C₂	semidirect
2. C₂²×C₃²×#67	C₂	semidirect
3. C₂×C₃²×D₃×D₄	C₂	semidirect
4. C₃²×#953	C₂	semidirect
5. C₃²×#940	C₂	semidirect
6. C₃²×#939	C₂	semidirect
7. C₃²×#938	C₂	semidirect
8. C₃²×#937	C₂	semidirect
9. C₃²×D₄×Dic₃	C₂	semidirect
10. C₃²×#930	C₂	semidirect
11. C₃²×C₄×#67	C₂	semidirect
13. C₃×D₄×#67	C₃	direct (N × H)
14. C₂⁴×C₃³	C₂²	semidirect
15. C₂³×C₃²×D₃	C₂²	semidirect
18. C₂×C₃³×D₄	C₂²	semidirect
19. C₂×C₃³×D₄	C₂²	semidirect
20. C₂²×C₃³×C₄	C₂²	semidirect
23. C₂×C₃²×#67	C₂²	semidirect
24. C₂×C₃²×#67	C₂²	semidirect
25. C₂×C₃²×#67	C₂²	semidirect
26. C₂×C₃²×#67	C₂²	semidirect
27. C₂×C₃²×#67	C₂²	semidirect
28. C₂²×C₃²×Dic₃	C₂²	semidirect
30. C₂×C₃²×D₁₂	C₂²	semidirect
31. C₂×C₃²×C₄×D₃	C₂²	semidirect
32. C₃²×#217	C₂²	semidirect
33. C₃²×#217	C₂²	semidirect
34. C₃²×#217	C₂²	semidirect
35. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₃²×C₄⋊Dic₃	C₂²	semidirect
38. C₃²×Dic₃⋊C₄	C₂²	semidirect
39. C₃²×C₄×Dic₃	C₂²	semidirect
43. C₂²×C₃²×D₄	D₃	semidirect
44. C₂²×C₃²×D₄	C₂×C₃	semidirect
45. C₂²×C₃×#67	C₂×C₃	semidirect
46. C₂×C₃×D₃×D₄	C₂×C₃	semidirect
55. C₃×#953	C₂×C₃	semidirect
56. C₃×#940	C₂×C₃	semidirect
57. C₃×#939	C₂×C₃	semidirect
58. C₃×#938	C₂×C₃	semidirect
59. C₃×#937	C₂×C₃	semidirect
60. C₃×D₄×Dic₃	C₂×C₃	semidirect
61. C₃×#930	C₂×C₃	semidirect
62. C₃×C₄×#67	C₂×C₃	semidirect
76. C₃³×D₄	D₄	semidirect
85. C₃²×#67	D₄	direct (N × H)
94. D₄×#67	C₃²	direct (N × H)
97. C₂⁴×C₃²	C₂×D₃	semidirect
98. C₂⁴×C₃²	C₂²×C₃	semidirect
99. C₂³×C₃×D₃	C₂²×C₃	semidirect
116. C₂×C₃²×D₄	C₂×D₃	semidirect
117. C₂×C₃²×D₄	C₂×D₃	semidirect
119. C₂×C₃²×D₄	C₂²×C₃	semidirect
120. C₂×C₃²×D₄	C₂²×C₃	semidirect
124. C₂²×C₃²×C₄	C₂×D₃	semidirect
125. C₂²×C₃²×C₄	C₂²×C₃	semidirect
128. C₂×C₃×#67	C₂²×C₃	semidirect
129. C₂×C₃×#67	C₂²×C₃	semidirect
130. C₂×C₃×#67	C₂²×C₃	semidirect
131. C₂×C₃×#67	C₂²×C₃	semidirect
132. C₂×C₃×#67	C₂²×C₃	semidirect
133. C₂²×C₃×Dic₃	C₂²×C₃	semidirect
135. C₂×C₃×D₁₂	C₂²×C₃	semidirect
136. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
145. C₃×#217	C₂²×C₃	semidirect
146. C₃×#217	C₂²×C₃	semidirect
147. C₃×#217	C₂²×C₃	semidirect
148. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
149. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
150. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
151. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
152. C₃×C₄×Dic₃	C₂²×C₃	semidirect
161. C₂²×C₃³	C₂×D₄	semidirect
162. C₂²×C₃³	C₂×D₄	semidirect
170. C₂×C₃²×D₃	C₂×D₄	semidirect
172. C₃³×C₄	C₂×D₄	semidirect
176. C₃²×Dic₃	C₂×D₄	semidirect
180. C₂²×C₃×D₄	C₃×D₃	semidirect
181. C₂²×C₃×D₄	C₂×C₃²	semidirect
182. C₂²×#67	C₂×C₃²	semidirect
183. C₂×D₃×D₄	C₂×C₃²	semidirect
192. #953	C₂×C₃²	semidirect
193. #940	C₂×C₃²	semidirect
194. #939	C₂×C₃²	semidirect
195. #938	C₂×C₃²	semidirect
196. #937	C₂×C₃²	semidirect
197. D₄×Dic₃	C₂×C₃²	semidirect
198. #930	C₂×C₃²	semidirect
199. C₄×#67	C₂×C₃²	semidirect
242. C₃²×D₄	#67	direct (N × H)
243. C₃²×D₄	C₃×D₄	semidirect
264. C₃×#67	C₃×D₄	direct (N × H)
283. C₂⁴×C₃	C₂×C₃×D₃	semidirect
284. C₂⁴×C₃	C₂²×C₃²	semidirect
285. C₂³×D₃	C₂²×C₃²	semidirect
302. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
303. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
305. C₂×C₃×D₄	C₂²×C₃²	semidirect
306. C₂×C₃×D₄	C₂²×C₃²	semidirect
310. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
311. C₂²×C₃×C₄	C₂²×C₃²	semidirect
314. C₂×#67	C₂²×C₃²	semidirect
315. C₂×#67	C₂²×C₃²	semidirect
316. C₂×#67	C₂²×C₃²	semidirect
317. C₂×#67	C₂²×C₃²	semidirect
318. C₂×#67	C₂²×C₃²	semidirect
319. C₂²×Dic₃	C₂²×C₃²	semidirect
321. C₂×D₁₂	C₂²×C₃²	semidirect
322. C₂×C₄×D₃	C₂²×C₃²	semidirect
331. #217	C₂²×C₃²	semidirect
332. #217	C₂²×C₃²	semidirect
333. #217	C₂²×C₃²	semidirect
334. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
335. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
336. C₄⋊Dic₃	C₂²×C₃²	semidirect
337. Dic₃⋊C₄	C₂²×C₃²	semidirect
338. C₄×Dic₃	C₂²×C₃²	semidirect
373. C₂²×C₃²	D₃×D₄	semidirect
374. C₂²×C₃²	C₂×#67	semidirect
375. C₂²×C₃²	C₂×C₃×D₄	semidirect
376. C₂²×C₃²	C₂×C₃×D₄	semidirect
385. C₂×C₃×D₃	C₂×C₃×D₄	semidirect
394. C₃²×C₄	C₂×#67	semidirect
395. C₃²×C₄	C₂×C₃×D₄	semidirect
399. C₃×Dic₃	C₂×C₃×D₄	semidirect
402. C₂²×D₄	C₃²×D₃	semidirect
411. C₃³	D₄²	semidirect
454. C₃×D₄	C₃×#67	direct (N × H)
455. C₃×D₄	C₃²×D₄	semidirect
476. #67	C₃²×D₄	direct (N × H)
507. C₂⁴	C₂×C₃²×D₃	semidirect
519. C₂×D₄	C₂×C₃²×D₃	semidirect
520. C₂×D₄	C₂×C₃²×D₃	semidirect
523. C₂²×C₄	C₂×C₃²×D₃	semidirect
566. C₂²×C₃	C₃×D₃×D₄	semidirect
567. C₂²×C₃	C₂×C₃×#67	semidirect
568. C₂²×C₃	C₂×C₃²×D₄	semidirect
569. C₂²×C₃	C₂×C₃²×D₄	semidirect
578. C₂×D₃	C₂×C₃²×D₄	semidirect
587. C₃×C₄	C₂×C₃×#67	semidirect
588. C₃×C₄	C₂×C₃²×D₄	semidirect
592. Dic₃	C₂×C₃²×D₄	semidirect
594. C₃²	D₄×#67	direct (N × H)
595. C₃²	C₃×D₄²	semidirect
616. D₄	C₃²×#67	direct (N × H)
663. C₂²	C₃²×D₃×D₄	semidirect
664. C₂²	C₂×C₃²×#67	semidirect
671. C₄	C₂×C₃²×#67	semidirect
673. C₃	C₃×D₄×#67	direct (N × H)
674. C₃	C₃²×D₄²	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃³×D₄	2
C₂²×C₃²×#67	2
C₂×C₃²×D₃×D₄	2
C₃²×#953	2
C₃²×#940	2
C₃²×#939	2
C₃²×#938	2
C₃²×#937	2
C₃²×D₄×Dic₃	2
C₃²×#930	2
C₃²×C₄×#67	2
C₃²×D₄²	3
C₃×D₄×#67	3

Subgroups — C32×D4×#67 #13179180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₄×#67 #13179180