Subgroups — C₂×C₃×#5683 #11910206

Order 1152.

2981 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#947	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#937	C₂	1	2	yes	maximal, complemented
4	C₃×#5683	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#885	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#882	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#875	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×H(3,𝔽₄)	—	3	1	no	maximal
9	C₂×#5683	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
11	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×#67	C₂²	1	4	yes	—
14	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
15	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
16	C₂²×C₃×Dic₆	C₂²	1	2	yes	complemented
17	C₃²×#124	C₂²	1	8	yes	complemented
18	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	complemented
19	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×#217	C₂²	1	2	yes	complemented
21	C₃×#947	C₂²	1	16	yes	complemented
22	C₃×#937	C₂²	1	16	yes	complemented
23	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
24	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
25	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
26	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
27	C₃×#885	C₂²	1	32	yes	complemented
28	C₃×#882	C₂²	1	32	yes	complemented
29	C₃×#875	C₂²	1	16	yes	complemented
30	C₃×H(3,𝔽₄)	—	3	16	no	—
31	C₂×C₃×#124	—	2	1	no	—
32	C₂×C₃×#124	—	3	2	no	—
33	C₂×C₃×#124	—	3	4	no	—
34	C₂×C₃×#124	—	3	2	no	—
35	C₂×C₃×#124	D₃	1	1	yes	characteristic, complemented
36	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×C₃×#120	—	3	2	no	—
38	C₂×C₃×#120	—	3	4	no	—
39	C₂×#947	C₂×C₃	1	2	yes	complemented
40	C₂×#937	C₂×C₃	1	2	yes	complemented
41	#5683	C₂×C₃	1	16	yes	direct product factor
42	C₂×#885	C₂×C₃	1	4	yes	complemented
43	C₂×#882	C₂×C₃	1	4	yes	complemented
44	C₂×#875	C₂×C₃	1	2	yes	complemented
45	C₂⁴×C₃²	C₂³	1	2	yes	—
46	C₂³×C₃×D₃	—	4	4	no	—
47	C₂³×C₃×D₃	—	4	8	no	—
48	C₂³×C₃×D₃	C₂³	1	4	yes	—
49	C₂³×C₃×D₃	C₂³	1	8	yes	complemented
50	C₂×C₃²×Q₈	—	4	2	no	—
51	C₂×C₃²×Q₈	C₂³	1	4	yes	complemented
52	C₂×C₃²×D₄	—	4	2	no	—
53	C₂×C₃²×D₄	C₂³	1	4	yes	—
54	C₂²×C₃²×C₄	C₂³	1	2	yes	—
55	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃²×C₄	C₂³	1	2	yes	—
57	C₂×C₃×#67	—	4	8	no	—
58	C₂×C₃×#67	C₂³	1	16	yes	—
59	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
60	C₂×C₃×D₁₂	—	4	4	no	—
61	C₂×C₃×D₁₂	—	4	4	no	—
62	C₂×C₃×D₁₂	C₂³	1	8	yes	—
63	C₂×C₃×D₁₂	C₂³	1	8	yes	—
64	C₂×C₃×Dic₆	—	4	4	no	—
65	C₂×C₃×Dic₆	C₂³	1	8	yes	complemented
66	C₃²×C₂²⋊C₄	C₂³	1	16	yes	complemented
67	C₃²×C₄²	C₂³	1	4	yes	complemented
68	C₃×#217	C₂³	1	8	yes	complemented
69	C₃×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
70	C₃×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
71	C₃×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
72	C₃×C₄×Dic₃	C₂³	1	8	yes	complemented
73	C₂×H(3,𝔽₄)	—	3	1	no	Sylow
74	C₂⁵×C₃	—	3	2	no	—
75	C₂⁴×D₃	C₂²×C₃	1	2	yes	complemented
76	C₂²×C₃×Q₈	—	2	1	no	—
77	C₂²×C₃×Q₈	—	3	2	no	—
78	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
79	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₂²×C₃×D₄	—	2	1	no	—
81	C₂²×C₃×D₄	—	3	4	no	—
82	C₂²×C₃×D₄	—	3	2	no	—
83	C₂²×C₃×D₄	—	3	2	no	—
84	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
86	C₂²×#67	C₂²×C₃	1	4	yes	—
87	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
88	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
89	C₂²×Dic₆	C₂²×C₃	1	2	yes	complemented
90	C₃×#124	—	2	8	no	—
91	C₃×#124	—	3	16	no	—
92	C₃×#124	—	3	32	no	—
93	C₃×#124	—	3	16	no	—
94	C₃×#124	C₂×D₃	1	8	yes	complemented
95	C₃×#124	C₂²×C₃	1	8	yes	complemented
96	C₃×#120	—	3	16	no	—
97	C₃×#120	—	3	32	no	—
98	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
99	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
100	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
101	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
102	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
103	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
104	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
105	C₂×C₃×C₄²	—	2	1	no	—
106	C₂×C₃×C₄²	—	3	2	no	—
107	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
108	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
109	C₂×#217	C₂²×C₃	1	2	yes	complemented
110	#947	C₂²×C₃	1	16	yes	complemented
111	#937	C₂²×C₃	1	16	yes	complemented
112	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	complemented
113	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	complemented
114	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	complemented
115	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
116	#885	C₂²×C₃	1	32	yes	complemented
117	#882	C₂²×C₃	1	32	yes	complemented
118	#875	C₂²×C₃	1	16	yes	complemented
119	C₂³×C₃²	—	2	8	no	—
120	C₂³×C₃²	—	2	4	no	—
121	C₂³×C₃²	C₂⁴	1	4	yes	—
122	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
123	C₂²×C₃×D₃	—	2	8	no	—
124	C₂²×C₃×D₃	—	2	8	no	—
125	C₂²×C₃×D₃	—	2	8	no	—
126	C₂²×C₃×D₃	—	4	8	no	—
127	C₂²×C₃×D₃	—	4	16	no	—
128	C₂²×C₃×D₃	—	4	32	no	—
129	C₂²×C₃×D₃	C₂⁴	1	8	yes	—
130	C₃²×Q₈	—	4	4	no	—
131	C₃²×D₄	—	4	4	no	—
132	C₂×C₃²×C₄	—	2	2	no	—
133	C₂×C₃²×C₄	—	2	4	no	—
134	C₂×C₃²×C₄	—	2	4	no	—
135	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
136	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
137	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
138	C₃×#67	—	4	16	no	—
139	C₂×C₃×Dic₃	—	2	8	no	—
140	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
141	C₃×D₁₂	—	4	8	no	—
142	C₃×D₁₂	—	4	8	no	—
143	C₃×Dic₆	—	4	8	no	—
144	H(3,𝔽₄)	—	3	16	no	—
145	C₂×#124	—	3	2	no	—
146	C₂×#124	—	3	4	no	—
147	C₂×#124	—	3	2	no	—
148	C₂×#124	C₃×D₃	1	1	yes	characteristic, complemented
149	C₂×#120	—	3	2	no	—
150	C₂×#120	—	3	4	no	—
151	C₂⁴×C₃	—	2	2	no	—
152	C₂⁴×C₃	—	3	4	no	—
153	C₂⁴×C₃	—	3	8	no	—
154	C₂⁴×C₃	—	12	4	no	—
155	C₂⁴×C₃	—	12	8	no	—
156	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
157	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
158	C₂³×D₃	—	4	4	no	—
159	C₂³×D₃	—	4	8	no	—
160	C₂³×D₃	C₂³×C₃	1	4	yes	—
161	C₂³×D₃	C₂³×C₃	1	8	yes	complemented
162	C₂×C₃×Q₈	—	2	4	no	—
163	C₂×C₃×Q₈	—	3	8	no	—
164	C₂×C₃×Q₈	—	4	2	no	—
165	C₂×C₃×Q₈	—	4	2	no	—
166	C₂×C₃×Q₈	—	4	4	no	—
167	C₂×C₃×Q₈	—	12	4	no	—
168	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	complemented
169	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	complemented
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	—	3	16	no	—
172	C₂×C₃×D₄	—	3	8	no	—
173	C₂×C₃×D₄	—	3	8	no	—
174	C₂×C₃×D₄	—	4	2	no	—
175	C₂×C₃×D₄	—	4	2	no	—
176	C₂×C₃×D₄	—	4	4	no	—
177	C₂×C₃×D₄	—	12	4	no	—
178	C₂×C₃×D₄	—	12	4	no	—
179	C₂×C₃×D₄	—	12	8	no	—
180	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
181	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	2	no	—
184	C₂²×C₃×C₄	—	2	2	no	—
185	C₂²×C₃×C₄	—	3	4	no	—
186	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
187	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
189	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
190	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
192	C₂×#67	—	4	8	no	—
193	C₂×#67	C₂³×C₃	1	16	yes	—
194	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
195	C₂×D₁₂	—	4	4	no	—
196	C₂×D₁₂	—	4	4	no	—
197	C₂×D₁₂	C₂³×C₃	1	8	yes	—
198	C₂×D₁₂	C₂³×C₃	1	8	yes	—
199	C₂×Dic₆	—	4	4	no	—
200	C₂×Dic₆	C₂³×C₃	1	8	yes	complemented
201	C₃×C₂²⋊C₄	—	2	16	no	—
202	C₃×C₂²⋊C₄	—	3	8	no	—
203	C₃×C₂²⋊C₄	—	3	16	no	—
204	C₃×C₂²⋊C₄	—	3	16	no	—
205	C₃×C₂²⋊C₄	—	3	16	no	—
206	C₃×C₂²⋊C₄	C₂²×D₃	1	16	yes	complemented
207	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
208	C₃×C₄²	—	2	4	no	—
209	C₃×C₄²	—	3	8	no	—
210	C₃×C₄²	C₂²×D₃	1	4	yes	complemented
211	C₃×C₄²	C₂³×C₃	1	4	yes	complemented
212	#217	C₂³×C₃	1	8	yes	complemented
213	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	complemented
214	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	complemented
215	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	complemented
216	C₄×Dic₃	C₂³×C₃	1	8	yes	complemented
217	C₂²×C₃²	—	2	8	no	—
218	C₂²×C₃²	—	2	4	no	—
219	C₂²×C₃²	—	4	8	no	—
220	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
221	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	—
222	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
223	C₂×C₃×D₃	—	2	8	no	—
224	C₂×C₃×D₃	—	2	8	no	—
225	C₂×C₃×D₃	—	2	8	no	—
226	C₂×C₃×D₃	—	4	32	no	—
227	C₂×C₃×D₃	—	4	16	no	—
228	C₃²×C₄	—	2	2	no	—
229	C₃²×C₄	—	2	4	no	—
230	C₃²×C₄	—	2	4	no	—
231	C₃×Dic₃	—	2	8	no	—
232	C₂⁵	—	3	2	no	—
233	C₂²×Q₈	—	3	2	no	—
234	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
235	C₂²×D₄	—	3	4	no	—
236	C₂²×D₄	—	3	2	no	—
237	C₂²×D₄	—	3	2	no	—
238	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
239	#124	—	3	16	no	—
240	#124	—	3	32	no	—
241	#124	—	3	16	no	—
242	#124	C₂×C₃×D₃	1	8	yes	complemented
243	#120	—	3	16	no	—
244	#120	—	3	32	no	—
245	C₂×C₂²⋊C₄	—	3	2	no	—
246	C₂×C₂²⋊C₄	—	3	4	no	—
247	C₂×C₂²⋊C₄	—	3	4	no	—
248	C₂×C₂²⋊C₄	—	3	4	no	—
249	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
250	C₂×C₄²	—	3	2	no	—
251	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
252	C₂³×C₃	—	2	4	no	—
253	C₂³×C₃	—	2	8	no	—
254	C₂³×C₃	—	2	8	no	—
255	C₂³×C₃	—	2	4	no	—
256	C₂³×C₃	—	2	1	no	—
257	C₂³×C₃	—	2	4	no	—
258	C₂³×C₃	—	3	8	no	—
259	C₂³×C₃	—	4	4	no	—
260	C₂³×C₃	—	4	8	no	—
261	C₂³×C₃	—	6	8	no	—
262	C₂³×C₃	—	6	8	no	—
263	C₂³×C₃	—	6	8	no	—
264	C₂³×C₃	—	12	8	no	—
265	C₂³×C₃	—	12	16	no	—
266	C₂³×C₃	—	12	32	no	—
267	C₂³×C₃	C₂³×D₃	1	4	yes	—
268	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
269	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
270	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
271	C₂²×D₃	—	2	8	no	—
272	C₂²×D₃	—	2	8	no	—
273	C₂²×D₃	—	2	8	no	—
274	C₂²×D₃	—	4	8	no	—
275	C₂²×D₃	—	4	16	no	—
276	C₂²×D₃	—	4	32	no	—
277	C₂²×D₃	C₂⁴×C₃	1	8	yes	—
278	C₃×Q₈	—	4	4	no	—
279	C₃×Q₈	—	4	4	no	—
280	C₃×Q₈	—	4	8	no	—
281	C₃×Q₈	—	12	8	no	—
282	C₃×D₄	—	4	4	no	—
283	C₃×D₄	—	4	4	no	—
284	C₃×D₄	—	4	8	no	—
285	C₃×D₄	—	12	8	no	—
286	C₃×D₄	—	12	8	no	—
287	C₃×D₄	—	12	16	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	4	no	—
298	C₂×C₃×C₄	—	3	8	no	—
299	C₂×C₃×C₄	—	4	4	no	—
300	C₂×C₃×C₄	—	4	4	no	—
301	C₂×C₃×C₄	—	6	8	no	—
302	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
303	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
304	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
305	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
306	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
307	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
308	#67	—	4	16	no	—
309	C₂×Dic₃	—	2	8	no	—
310	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
311	D₁₂	—	4	8	no	—
312	D₁₂	—	4	8	no	—
313	Dic₆	—	4	8	no	—
314	C₂×C₃²	—	4	4	no	—
315	C₂×C₃²	H(3,𝔽₄)	1	4	yes	complemented
316	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
318	C₃×D₃	—	4	8	no	—
319	C₂⁴	—	3	4	no	—
320	C₂⁴	—	3	8	no	—
321	C₂⁴	—	12	4	no	—
322	C₂⁴	—	12	8	no	—
323	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
324	C₂×Q₈	—	3	8	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	12	4	no	—
327	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	complemented
328	C₂×D₄	—	3	16	no	—
329	C₂×D₄	—	3	8	no	—
330	C₂×D₄	—	3	8	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	12	4	no	—
333	C₂×D₄	—	12	4	no	—
334	C₂×D₄	—	12	8	no	—
335	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
336	C₂²×C₄	—	3	4	no	—
337	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
338	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
340	C₂²⋊C₄	—	3	8	no	—
341	C₂²⋊C₄	—	3	16	no	—
342	C₂²⋊C₄	—	3	16	no	—
343	C₂²⋊C₄	—	3	16	no	—
344	C₂²⋊C₄	C₂²×C₃×D₃	1	16	yes	complemented
345	C₄²	—	3	8	no	—
346	C₄²	C₂²×C₃×D₃	1	4	yes	complemented
347	C₂²×C₃	—	2	4	no	—
348	C₂²×C₃	—	2	8	no	—
349	C₂²×C₃	—	2	8	no	—
350	C₂²×C₃	—	2	4	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	4	no	—
353	C₂²×C₃	—	2	1	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	—	4	8	no	—
356	C₂²×C₃	—	4	8	no	—
357	C₂²×C₃	—	4	8	no	—
358	C₂²×C₃	—	6	8	no	—
359	C₂²×C₃	—	6	8	no	—
360	C₂²×C₃	—	6	8	no	—
361	C₂²×C₃	—	8	8	no	—
362	C₂²×C₃	—	12	32	no	—
363	C₂²×C₃	—	12	16	no	—
364	C₂²×C₃	#1004	1	2	yes	—
365	C₂²×C₃	#1009	1	4	yes	—
366	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
367	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
368	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
369	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
370	C₂×D₃	—	2	8	no	—
371	C₂×D₃	—	2	8	no	—
372	C₂×D₃	—	2	8	no	—
373	C₂×D₃	—	4	32	no	—
374	C₂×D₃	—	4	16	no	—
375	C₃×C₄	—	2	4	no	—
376	C₃×C₄	—	2	2	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	2	4	no	—
379	C₃×C₄	—	2	4	no	—
380	C₃×C₄	—	2	4	no	—
381	C₃×C₄	—	2	2	no	—
382	C₃×C₄	—	4	4	no	—
383	C₃×C₄	—	4	4	no	—
384	C₃×C₄	—	6	8	no	—
385	Dic₃	—	2	8	no	—
386	C₃²	C₂×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Sylow
387	C₂³	—	2	4	no	—
388	C₂³	—	2	8	no	—
389	C₂³	—	3	8	no	—
390	C₂³	—	6	8	no	—
391	C₂³	—	6	8	no	—
392	C₂³	—	6	8	no	—
393	C₂³	—	12	8	no	—
394	C₂³	—	12	16	no	—
395	C₂³	—	12	32	no	—
396	C₂³	C₂³×C₃×D₃	1	4	yes	—
397	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
398	Q₈	—	4	4	no	—
399	Q₈	—	12	8	no	—
400	D₄	—	4	4	no	—
401	D₄	—	12	8	no	—
402	D₄	—	12	8	no	—
403	D₄	—	12	16	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	3	8	no	—
408	C₂×C₄	—	6	8	no	—
409	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
410	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
411	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
412	C₂×C₃	—	2	1	no	—
413	C₂×C₃	—	2	2	no	—
414	C₂×C₃	—	2	4	no	—
415	C₂×C₃	—	4	4	no	—
416	C₂×C₃	—	4	4	no	—
417	C₂×C₃	—	8	4	no	—
418	C₂×C₃	—	12	8	no	—
419	C₂×C₃	#5683	1	4	yes	direct product factor
420	C₂×C₃	C₃×H(3,𝔽₄)	1	4	yes	complemented
421	C₂×C₃	C₂×#1004	1	1	yes	characteristic
422	C₂×C₃	C₂×#1009	1	2	yes	—
423	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
425	D₃	—	4	8	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	8	no	—
428	C₂²	—	4	8	no	—
429	C₂²	—	6	8	no	—
430	C₂²	—	6	8	no	—
431	C₂²	—	6	8	no	—
432	C₂²	—	12	32	no	—
433	C₂²	—	12	16	no	—
434	C₂²	C₃×#1004	1	2	yes	—
435	C₂²	C₃×#1009	1	4	yes	—
436	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	4	no	—
440	C₄	—	6	8	no	—
441	C₃	—	2	1	no	—
442	C₃	C₂×#5683	1	1	yes	characteristic, direct product factor
443	C₃	C₂×C₃×H(3,𝔽₄)	1	1	yes	characteristic, complemented
444	C₂	—	4	4	no	—
445	C₂	—	12	8	no	—
446	C₂	C₃×#5683	1	4	yes	direct product factor
447	C₂	C₂×C₃×#1004	1	1	yes	characteristic
448	C₂	C₂×C₃×#1009	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#124	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#124	D₃
hypocenter	C₃	C₂×C₃×H(3,𝔽₄)
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#124	C₂	semidirect
2. C₂×C₃×#947	C₂	semidirect
3. C₂×C₃×#937	C₂	semidirect
4. C₃×#5683	C₂	direct (N × H)
5. C₂×C₃×#885	C₂	semidirect
6. C₂×C₃×#882	C₂	semidirect
7. C₂×C₃×#875	C₂	semidirect
9. C₂×#5683	C₃	direct (N × H)
10. C₂⁴×C₃×D₃	C₂²	semidirect
11. C₂²×C₃²×Q₈	C₂²	semidirect
16. C₂²×C₃×Dic₆	C₂²	semidirect
17. C₃²×#124	C₂²	semidirect
18. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
19. C₂×C₃²×C₄²	C₂²	semidirect
20. C₂×C₃×#217	C₂²	semidirect
21. C₃×#947	C₂²	semidirect
22. C₃×#937	C₂²	semidirect
23. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
24. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
25. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
26. C₂×C₃×C₄×Dic₃	C₂²	semidirect
27. C₃×#885	C₂²	semidirect
28. C₃×#882	C₂²	semidirect
29. C₃×#875	C₂²	semidirect
35. C₂×C₃×#124	D₃	semidirect
36. C₂×C₃×#124	C₂×C₃	semidirect
39. C₂×#947	C₂×C₃	semidirect
40. C₂×#937	C₂×C₃	semidirect
41. #5683	C₂×C₃	direct (N × H)
42. C₂×#885	C₂×C₃	semidirect
43. C₂×#882	C₂×C₃	semidirect
44. C₂×#875	C₂×C₃	semidirect
49. C₂³×C₃×D₃	C₂³	semidirect
51. C₂×C₃²×Q₈	C₂³	semidirect
65. C₂×C₃×Dic₆	C₂³	semidirect
66. C₃²×C₂²⋊C₄	C₂³	semidirect
67. C₃²×C₄²	C₂³	semidirect
68. C₃×#217	C₂³	semidirect
69. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
70. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
71. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
72. C₃×C₄×Dic₃	C₂³	semidirect
75. C₂⁴×D₃	C₂²×C₃	semidirect
78. C₂²×C₃×Q₈	C₂×D₃	semidirect
79. C₂²×C₃×Q₈	C₂²×C₃	semidirect
89. C₂²×Dic₆	C₂²×C₃	semidirect
94. C₃×#124	C₂×D₃	semidirect
95. C₃×#124	C₂²×C₃	semidirect
103. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
104. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
107. C₂×C₃×C₄²	C₂×D₃	semidirect
108. C₂×C₃×C₄²	C₂²×C₃	semidirect
109. C₂×#217	C₂²×C₃	semidirect
110. #947	C₂²×C₃	semidirect
111. #937	C₂²×C₃	semidirect
112. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
113. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
114. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
115. C₂×C₄×Dic₃	C₂²×C₃	semidirect
116. #885	C₂²×C₃	semidirect
117. #882	C₂²×C₃	semidirect
118. #875	C₂²×C₃	semidirect
148. C₂×#124	C₃×D₃	semidirect
161. C₂³×D₃	C₂³×C₃	semidirect
168. C₂×C₃×Q₈	C₂²×D₃	semidirect
169. C₂×C₃×Q₈	C₂³×C₃	semidirect
200. C₂×Dic₆	C₂³×C₃	semidirect
206. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
207. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
210. C₃×C₄²	C₂²×D₃	semidirect
211. C₃×C₄²	C₂³×C₃	semidirect
212. #217	C₂³×C₃	semidirect
213. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
214. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
215. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
216. C₄×Dic₃	C₂³×C₃	semidirect
234. C₂²×Q₈	C₂×C₃×D₃	semidirect
242. #124	C₂×C₃×D₃	semidirect
249. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
251. C₂×C₄²	C₂×C₃×D₃	semidirect
315. C₂×C₃²	H(3,𝔽₄)	semidirect
327. C₂×Q₈	C₂²×C₃×D₃	semidirect
344. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
346. C₄²	C₂²×C₃×D₃	semidirect
386. C₃²	C₂×H(3,𝔽₄)	semidirect
419. C₂×C₃	#5683	direct (N × H)
420. C₂×C₃	C₃×H(3,𝔽₄)	semidirect
442. C₃	C₂×#5683	direct (N × H)
443. C₃	C₂×C₃×H(3,𝔽₄)	semidirect
446. C₂	C₃×#5683	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×C₃²×#124	2
C₂×C₃×#947	2
C₂×C₃×#937	2
C₃×#5683	2
C₂×C₃×#885	2
C₂×C₃×#882	2
C₂×C₃×#875	2
C₂×C₃×H(3,𝔽₄)	3
C₂×#5683	3

Subgroups — C2×C3×#5683 #11910206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5683 #11910206