Subgroups — C₃²×#5634 #13179013

Order 1728.

1748 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#946	C₂	1	2	yes	maximal, complemented
3	C₂×C₃²×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃²×#924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#897	C₂	1	2	yes	maximal, complemented
6	C₃²×#896	C₂	1	2	yes	maximal, complemented
7	C₃²×#896	C₂	1	2	yes	maximal, complemented
8	C₃²×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal
9	C₃²×#878	C₂	1	2	yes	maximal, complemented
10	C₃²×#543	—	3	1	no	maximal
11	C₃×#5634	C₃	1	4	yes	maximal, direct product factor
12	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
13	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
17	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
18	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃²×Dic₆	C₂²	1	2	yes	complemented
20	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
21	C₃³×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃²×#217	C₂²	1	2	yes	—
24	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
29	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	complemented
30	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	complemented
31	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	complemented
32	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	complemented
33	C₃²×C₂²⋊Q₈	—	2	4	no	—
34	C₃²×C₂²⋊Q₈	—	3	2	no	—
35	C₃²×C₂²⋊Q₈	—	3	1	no	—
36	C₃²×C₂²⋊Q₈	—	3	2	no	—
37	C₃²×C₂²⋊Q₈	—	3	2	no	—
38	C₃²×C₂²⋊Q₈	—	3	2	no	—
39	C₃²×C₂²⋊Q₈	—	3	2	no	—
40	C₃²×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
41	C₃²×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
42	C₂×C₃²×C₂²⋊C₄	—	3	1	no	—
43	C₂×C₃²×C₂²⋊C₄	—	3	2	no	—
44	C₃×#946	C₂×C₃	1	8	yes	complemented
45	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	4	yes	—
46	C₃×#924	C₂×C₃	1	4	yes	complemented
47	C₃×#897	C₂×C₃	1	8	yes	complemented
48	C₃×#896	C₂×C₃	1	8	yes	complemented
49	C₃×#896	C₂×C₃	1	8	yes	complemented
50	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	8	yes	—
51	C₃×#878	C₂×C₃	1	8	yes	complemented
52	C₂³×C₃³	C₂³	1	1	yes	characteristic
53	C₂²×C₃²×D₃	—	4	1	no	—
54	C₂²×C₃²×D₃	—	4	1	no	—
55	C₂²×C₃²×D₃	Q₈	1	4	yes	complemented
56	C₂²×C₃²×D₃	C₂³	1	2	yes	—
57	C₃³×Q₈	—	4	1	no	—
58	C₂×C₃³×C₄	—	4	1	no	—
59	C₂×C₃³×C₄	C₂³	1	2	yes	—
60	C₂×C₃³×C₄	C₂³	1	2	yes	—
61	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
62	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
63	C₂×C₃²×Dic₃	—	4	1	no	—
64	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
65	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
66	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
67	C₃²×C₄×D₃	—	4	2	no	—
68	C₃²×C₄×D₃	—	4	2	no	—
69	C₃²×Dic₆	—	4	1	no	—
70	C₃²×Dic₆	—	4	2	no	—
71	C₃×#543	—	3	4	no	—
72	#5634	C₃²	1	1	yes	characteristic, direct product factor
73	C₂⁴×C₃²	—	3	1	no	—
74	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	—
75	C₂×C₃²×Q₈	—	2	4	no	—
76	C₂×C₃²×Q₈	—	3	1	no	—
77	C₂×C₃²×Q₈	—	3	2	no	—
78	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
79	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
80	C₂²×C₃²×C₄	—	2	4	no	—
81	C₂²×C₃²×C₄	—	3	1	no	—
82	C₂²×C₃²×C₄	—	3	2	no	—
83	C₂²×C₃²×C₄	—	3	2	no	—
84	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
86	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
87	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
88	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
89	C₂×C₃×Dic₆	C₂²×C₃	1	8	yes	complemented
90	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	complemented
91	C₃²×C₄⋊C₄	—	2	4	no	—
92	C₃²×C₄⋊C₄	—	2	8	no	—
93	C₃²×C₄⋊C₄	—	3	2	no	—
94	C₃²×C₄⋊C₄	—	3	2	no	—
95	C₃²×C₄⋊C₄	—	3	2	no	—
96	C₃²×C₄⋊C₄	—	3	1	no	—
97	C₃²×C₄⋊C₄	—	3	2	no	—
98	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
99	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
100	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
101	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
102	C₃²×C₂²⋊C₄	—	2	8	no	—
103	C₃²×C₂²⋊C₄	—	3	2	no	—
104	C₃²×C₂²⋊C₄	—	3	2	no	—
105	C₃²×C₂²⋊C₄	—	3	2	no	—
106	C₃²×C₂²⋊C₄	—	3	2	no	—
107	C₃²×C₂²⋊C₄	—	3	2	no	—
108	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
109	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
110	C₃×#217	C₂²×C₃	1	8	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
112	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
113	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
114	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
115	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	complemented
116	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	complemented
117	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	complemented
118	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	complemented
119	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	complemented
120	C₂²×C₃³	—	2	1	no	—
121	C₂²×C₃³	—	2	1	no	—
122	C₂²×C₃³	C₂×Q₈	1	2	yes	—
123	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
124	C₂×C₃²×D₃	—	2	2	no	—
125	C₂×C₃²×D₃	—	2	2	no	—
126	C₂×C₃²×D₃	—	4	4	no	—
127	C₂×C₃²×D₃	C₂×Q₈	1	4	yes	—
128	C₃³×C₄	—	2	1	no	—
129	C₃³×C₄	—	2	2	no	—
130	C₃³×C₄	—	2	1	no	—
131	C₃³×C₄	—	2	2	no	—
132	C₃²×Dic₃	—	2	2	no	—
133	C₃²×Dic₃	—	2	2	no	—
134	C₃²×Dic₃	—	2	2	no	—
135	C₃×C₂²⋊Q₈	—	2	4	no	—
136	C₃×C₂²⋊Q₈	—	3	8	no	—
137	C₃×C₂²⋊Q₈	—	3	4	no	—
138	C₃×C₂²⋊Q₈	—	3	8	no	—
139	C₃×C₂²⋊Q₈	—	3	8	no	—
140	C₃×C₂²⋊Q₈	—	3	8	no	—
141	C₃×C₂²⋊Q₈	—	3	8	no	—
142	C₃×C₂²⋊Q₈	C₃×D₃	1	4	yes	complemented
143	C₃×C₂²⋊Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
144	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
145	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
146	#946	C₂×C₃²	1	2	yes	complemented
147	C₂×(C₂×D₃)⋊C₄	C₂×C₃²	1	1	yes	characteristic
148	#924	C₂×C₃²	1	1	yes	characteristic, complemented
149	#897	C₂×C₃²	1	2	yes	complemented
150	#896	C₂×C₃²	1	2	yes	complemented
151	#896	C₂×C₃²	1	2	yes	complemented
152	D₃×C₂²⋊C₄	C₂×C₃²	1	2	yes	—
153	#878	C₂×C₃²	1	2	yes	complemented
154	C₂³×C₃²	—	2	4	no	—
155	C₂³×C₃²	—	3	2	no	—
156	C₂³×C₃²	—	3	4	no	—
157	C₂³×C₃²	—	12	1	no	—
158	C₂³×C₃²	—	12	1	no	—
159	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
160	C₂³×C₃²	C₂³×C₃	1	4	yes	—
161	C₂²×C₃×D₃	—	4	4	no	—
162	C₂²×C₃×D₃	—	4	4	no	—
163	C₂²×C₃×D₃	C₃×Q₈	1	16	yes	complemented
164	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
165	C₃²×Q₈	—	4	1	no	—
166	C₃²×Q₈	—	4	4	no	—
167	C₃²×Q₈	—	4	8	no	—
168	C₃²×Q₈	—	12	1	no	—
169	C₃²×Q₈	—	12	2	no	—
170	C₂×C₃²×C₄	—	2	4	no	—
171	C₂×C₃²×C₄	—	2	8	no	—
172	C₂×C₃²×C₄	—	2	8	no	—
173	C₂×C₃²×C₄	—	2	4	no	—
174	C₂×C₃²×C₄	—	3	2	no	—
175	C₂×C₃²×C₄	—	3	2	no	—
176	C₂×C₃²×C₄	—	3	2	no	—
177	C₂×C₃²×C₄	—	4	1	no	—
178	C₂×C₃²×C₄	—	4	4	no	—
179	C₂×C₃²×C₄	—	4	8	no	—
180	C₂×C₃²×C₄	—	12	2	no	—
181	C₂×C₃²×C₄	—	12	2	no	—
182	C₂×C₃²×C₄	—	12	1	no	—
183	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
184	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
185	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
186	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
187	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
188	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
189	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
190	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
191	C₂×C₃×Dic₃	—	4	4	no	—
192	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
193	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
194	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
195	C₃×C₄×D₃	—	4	8	no	—
196	C₃×C₄×D₃	—	4	8	no	—
197	C₃×Dic₆	—	4	4	no	—
198	C₃×Dic₆	—	4	8	no	—
199	#543	—	3	1	no	Sylow
200	C₂×C₃³	—	2	2	no	—
201	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
202	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
204	C₃²×D₃	—	2	4	no	—
205	C₂⁴×C₃	—	3	4	no	—
206	C₂³×D₃	C₂²×C₃²	1	1	yes	characteristic
207	C₂×C₃×Q₈	—	2	4	no	—
208	C₂×C₃×Q₈	—	3	4	no	—
209	C₂×C₃×Q₈	—	3	8	no	—
210	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
211	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
212	C₂²×C₃×C₄	—	2	4	no	—
213	C₂²×C₃×C₄	—	3	4	no	—
214	C₂²×C₃×C₄	—	3	8	no	—
215	C₂²×C₃×C₄	—	3	8	no	—
216	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
217	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
218	C₂²×Dic₃	C₂²×C₃²	1	1	yes	characteristic
219	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
220	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
221	C₂×Dic₆	C₂²×C₃²	1	2	yes	complemented
222	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic, complemented
223	C₃×C₄⋊C₄	—	2	4	no	—
224	C₃×C₄⋊C₄	—	2	8	no	—
225	C₃×C₄⋊C₄	—	3	8	no	—
226	C₃×C₄⋊C₄	—	3	8	no	—
227	C₃×C₄⋊C₄	—	3	8	no	—
228	C₃×C₄⋊C₄	—	3	4	no	—
229	C₃×C₄⋊C₄	—	3	8	no	—
230	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
231	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	complemented
232	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
233	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
234	C₃×C₂²⋊C₄	—	2	8	no	—
235	C₃×C₂²⋊C₄	—	3	8	no	—
236	C₃×C₂²⋊C₄	—	3	8	no	—
237	C₃×C₂²⋊C₄	—	3	8	no	—
238	C₃×C₂²⋊C₄	—	3	8	no	—
239	C₃×C₂²⋊C₄	—	3	8	no	—
240	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
241	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
242	#217	C₂²×C₃²	1	2	yes	—
243	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
244	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
245	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
246	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
247	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	complemented
248	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
249	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	complemented
250	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	complemented
251	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	complemented
252	C₂²×C₃²	—	2	1	no	—
253	C₂²×C₃²	—	2	1	no	—
254	C₂²×C₃²	—	2	4	no	—
255	C₂²×C₃²	—	2	8	no	—
256	C₂²×C₃²	—	2	4	no	—
257	C₂²×C₃²	—	2	4	no	—
258	C₂²×C₃²	—	3	4	no	—
259	C₂²×C₃²	—	4	4	no	—
260	C₂²×C₃²	—	4	4	no	—
261	C₂²×C₃²	—	6	2	no	—
262	C₂²×C₃²	—	6	2	no	—
263	C₂²×C₃²	—	12	4	no	—
264	C₂²×C₃²	D₃×Q₈	1	2	yes	—
265	C₂²×C₃²	C₂×C₃×Q₈	1	8	yes	—
266	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
267	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
268	C₂×C₃×D₃	—	2	8	no	—
269	C₂×C₃×D₃	—	2	8	no	—
270	C₂×C₃×D₃	—	4	16	no	—
271	C₂×C₃×D₃	C₂×C₃×Q₈	1	16	yes	—
272	C₃²×C₄	—	2	8	no	—
273	C₃²×C₄	—	2	1	no	—
274	C₃²×C₄	—	2	1	no	—
275	C₃²×C₄	—	2	2	no	—
276	C₃²×C₄	—	2	2	no	—
277	C₃²×C₄	—	2	4	no	—
278	C₃²×C₄	—	2	8	no	—
279	C₃²×C₄	—	2	4	no	—
280	C₃²×C₄	—	2	8	no	—
281	C₃²×C₄	—	4	8	no	—
282	C₃²×C₄	—	4	4	no	—
283	C₃²×C₄	—	4	8	no	—
284	C₃²×C₄	—	6	2	no	—
285	C₃²×C₄	—	6	2	no	—
286	C₃²×C₄	—	6	2	no	—
287	C₃×Dic₃	—	2	8	no	—
288	C₃×Dic₃	—	2	8	no	—
289	C₃×Dic₃	—	2	8	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	2	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	C₃²×D₃	1	1	yes	characteristic, complemented
297	C₂×C₂²⋊C₄	—	3	1	no	—
298	C₂×C₂²⋊C₄	—	3	2	no	—
299	C₃³	#543	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₃	—	2	4	no	—
301	C₂³×C₃	—	3	8	no	—
302	C₂³×C₃	—	3	16	no	—
303	C₂³×C₃	—	12	4	no	—
304	C₂³×C₃	—	12	4	no	—
305	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
306	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
307	C₂²×D₃	—	4	1	no	—
308	C₂²×D₃	—	4	1	no	—
309	C₂²×D₃	C₃²×Q₈	1	4	yes	complemented
310	C₂²×D₃	C₂³×C₃²	1	2	yes	—
311	C₃×Q₈	—	4	4	no	—
312	C₃×Q₈	—	4	1	no	—
313	C₃×Q₈	—	4	8	no	—
314	C₃×Q₈	—	12	4	no	—
315	C₃×Q₈	—	12	8	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	8	no	—
318	C₂×C₃×C₄	—	2	8	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	—	3	8	no	—
321	C₂×C₃×C₄	—	3	8	no	—
322	C₂×C₃×C₄	—	3	8	no	—
323	C₂×C₃×C₄	—	4	4	no	—
324	C₂×C₃×C₄	—	4	1	no	—
325	C₂×C₃×C₄	—	4	8	no	—
326	C₂×C₃×C₄	—	12	8	no	—
327	C₂×C₃×C₄	—	12	8	no	—
328	C₂×C₃×C₄	—	12	4	no	—
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
330	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
331	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
332	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
333	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
335	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
336	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
337	C₂×Dic₃	—	4	1	no	—
338	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
339	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
340	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
341	C₄×D₃	—	4	2	no	—
342	C₄×D₃	—	4	2	no	—
343	Dic₆	—	4	1	no	—
344	Dic₆	—	4	2	no	—
345	C₂×C₃²	—	2	2	no	—
346	C₂×C₃²	—	2	4	no	—
347	C₂×C₃²	—	2	4	no	—
348	C₂×C₃²	—	2	4	no	—
349	C₂×C₃²	—	2	8	no	—
350	C₂×C₃²	—	4	8	no	—
351	C₂×C₃²	—	6	4	no	—
352	C₂×C₃²	#1004	1	1	yes	characteristic
353	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
354	C₂×C₃²	#1009	1	1	yes	characteristic
355	C₂×C₃²	C₂²×C₃×Q₈	1	4	yes	—
356	C₂×C₃²	C₃×H(5,𝔽₂)	1	4	yes	—
357	C₂×C₃²	C₃×H(5,𝔽₂)	1	4	yes	—
358	C₃×D₃	—	2	16	no	—
359	C₂⁴	—	3	1	no	—
360	C₂×Q₈	—	3	1	no	—
361	C₂×Q₈	—	3	2	no	—
362	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	3	2	no	—
365	C₂²×C₄	—	3	2	no	—
366	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
367	C₄⋊C₄	—	3	2	no	—
368	C₄⋊C₄	—	3	2	no	—
369	C₄⋊C₄	—	3	2	no	—
370	C₄⋊C₄	—	3	1	no	—
371	C₄⋊C₄	—	3	2	no	—
372	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
373	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	complemented
374	C₂²⋊C₄	—	3	2	no	—
375	C₂²⋊C₄	—	3	2	no	—
376	C₂²⋊C₄	—	3	2	no	—
377	C₂²⋊C₄	—	3	2	no	—
378	C₂²⋊C₄	—	3	2	no	—
379	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	—
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	2	1	no	—
383	C₂²×C₃	—	2	1	no	—
384	C₂²×C₃	—	2	4	no	—
385	C₂²×C₃	—	2	8	no	—
386	C₂²×C₃	—	3	16	no	—
387	C₂²×C₃	—	4	4	no	—
388	C₂²×C₃	—	4	4	no	—
389	C₂²×C₃	—	6	8	no	—
390	C₂²×C₃	—	6	8	no	—
391	C₂²×C₃	—	12	16	no	—
392	C₂²×C₃	C₃×D₃×Q₈	1	8	yes	—
393	C₂²×C₃	C₂×C₃²×Q₈	1	2	yes	—
394	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
395	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
396	C₂×D₃	—	2	2	no	—
397	C₂×D₃	—	2	2	no	—
398	C₂×D₃	—	4	4	no	—
399	C₂×D₃	C₂×C₃²×Q₈	1	4	yes	—
400	C₃×C₄	—	2	8	no	—
401	C₃×C₄	—	2	4	no	—
402	C₃×C₄	—	2	4	no	—
403	C₃×C₄	—	2	8	no	—
404	C₃×C₄	—	2	8	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	2	no	—
408	C₃×C₄	—	2	1	no	—
409	C₃×C₄	—	4	4	no	—
410	C₃×C₄	—	4	8	no	—
411	C₃×C₄	—	4	8	no	—
412	C₃×C₄	—	6	8	no	—
413	C₃×C₄	—	6	8	no	—
414	C₃×C₄	—	6	8	no	—
415	Dic₃	—	2	2	no	—
416	Dic₃	—	2	2	no	—
417	Dic₃	—	2	2	no	—
418	C₃²	—	2	4	no	—
419	C₃²	#5634	1	1	yes	characteristic, direct product factor
420	C₃²	C₃×#543	1	4	yes	complemented
421	C₂³	—	3	2	no	—
422	C₂³	—	3	4	no	—
423	C₂³	—	12	1	no	—
424	C₂³	—	12	1	no	—
425	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
426	Q₈	—	4	1	no	—
427	Q₈	—	12	1	no	—
428	Q₈	—	12	2	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	3	2	no	—
431	C₂×C₄	—	3	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	12	2	no	—
434	C₂×C₄	—	12	2	no	—
435	C₂×C₄	—	12	1	no	—
436	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
437	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
439	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
440	C₂×C₃	—	2	8	no	—
441	C₂×C₃	—	2	2	no	—
442	C₂×C₃	—	2	4	no	—
443	C₂×C₃	—	2	4	no	—
444	C₂×C₃	—	2	4	no	—
445	C₂×C₃	—	4	8	no	—
446	C₂×C₃	—	6	16	no	—
447	C₂×C₃	C₃×#1004	1	4	yes	—
448	C₂×C₃	C₂×C₃×D₃×Q₈	1	4	yes	—
449	C₂×C₃	C₃×#1009	1	4	yes	—
450	C₂×C₃	C₂²×C₃²×Q₈	1	1	yes	characteristic
451	C₂×C₃	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₃	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
453	D₃	—	2	4	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	3	4	no	—
457	C₂²	—	6	2	no	—
458	C₂²	—	6	2	no	—
459	C₂²	—	12	4	no	—
460	C₂²	C₃²×D₃×Q₈	1	2	yes	—
461	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	6	2	no	—
467	C₄	—	6	2	no	—
468	C₄	—	6	2	no	—
469	C₃	—	2	4	no	—
470	C₃	C₃×#5634	1	4	yes	direct product factor
471	C₃	C₃²×#543	1	1	yes	characteristic, complemented
472	C₂	—	2	2	no	—
473	C₂	—	6	4	no	—
474	C₂	C₃²×#1004	1	1	yes	characteristic
475	C₂	C₂×C₃²×D₃×Q₈	1	1	yes	characteristic
476	C₂	C₃²×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×C₂²⋊Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂³×C₃²×D₃	C₂²
hypercenter	C₃²×C₂²⋊Q₈	D₃
hypocenter	C₃	C₃²×#543
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₂²⋊Q₈	C₂	semidirect
2. C₃²×#946	C₂	semidirect
4. C₃²×#924	C₂	semidirect
5. C₃²×#897	C₂	semidirect
6. C₃²×#896	C₂	semidirect
7. C₃²×#896	C₂	semidirect
9. C₃²×#878	C₂	semidirect
11. C₃×#5634	C₃	direct (N × H)
13. C₂×C₃³×Q₈	C₂²	semidirect
18. C₂×C₃²×Dic₆	C₂²	semidirect
19. C₂×C₃²×Dic₆	C₂²	semidirect
20. C₃³×C₄⋊C₄	C₂²	semidirect
21. C₃³×C₄⋊C₄	C₂²	semidirect
28. C₃²×C₄⋊Dic₃	C₂²	semidirect
29. C₃²×C₄⋊Dic₃	C₂²	semidirect
30. C₃²×Dic₃⋊C₄	C₂²	semidirect
31. C₃²×Dic₃⋊C₄	C₂²	semidirect
32. C₃²×Dic₃⋊C₄	C₂²	semidirect
40. C₃²×C₂²⋊Q₈	D₃	semidirect
41. C₃²×C₂²⋊Q₈	C₂×C₃	semidirect
44. C₃×#946	C₂×C₃	semidirect
46. C₃×#924	C₂×C₃	semidirect
47. C₃×#897	C₂×C₃	semidirect
48. C₃×#896	C₂×C₃	semidirect
49. C₃×#896	C₂×C₃	semidirect
51. C₃×#878	C₂×C₃	semidirect
55. C₂²×C₃²×D₃	Q₈	semidirect
72. #5634	C₃²	direct (N × H)
78. C₂×C₃²×Q₈	C₂×D₃	semidirect
79. C₂×C₃²×Q₈	C₂²×C₃	semidirect
89. C₂×C₃×Dic₆	C₂²×C₃	semidirect
90. C₂×C₃×Dic₆	C₂²×C₃	semidirect
98. C₃²×C₄⋊C₄	C₂×D₃	semidirect
99. C₃²×C₄⋊C₄	C₂×D₃	semidirect
100. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
101. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
115. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
116. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
117. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
118. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
119. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
142. C₃×C₂²⋊Q₈	C₃×D₃	semidirect
143. C₃×C₂²⋊Q₈	C₂×C₃²	semidirect
146. #946	C₂×C₃²	semidirect
148. #924	C₂×C₃²	semidirect
149. #897	C₂×C₃²	semidirect
150. #896	C₂×C₃²	semidirect
151. #896	C₂×C₃²	semidirect
153. #878	C₂×C₃²	semidirect
163. C₂²×C₃×D₃	C₃×Q₈	semidirect
210. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
211. C₂×C₃×Q₈	C₂²×C₃²	semidirect
221. C₂×Dic₆	C₂²×C₃²	semidirect
222. C₂×Dic₆	C₂²×C₃²	semidirect
230. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
231. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
232. C₃×C₄⋊C₄	C₂²×C₃²	semidirect
233. C₃×C₄⋊C₄	C₂²×C₃²	semidirect
247. C₄⋊Dic₃	C₂²×C₃²	semidirect
248. C₄⋊Dic₃	C₂²×C₃²	semidirect
249. Dic₃⋊C₄	C₂²×C₃²	semidirect
250. Dic₃⋊C₄	C₂²×C₃²	semidirect
251. Dic₃⋊C₄	C₂²×C₃²	semidirect
296. C₂²⋊Q₈	C₃²×D₃	semidirect
299. C₃³	#543	semidirect
309. C₂²×D₃	C₃²×Q₈	semidirect
362. C₂×Q₈	C₂×C₃²×D₃	semidirect
372. C₄⋊C₄	C₂×C₃²×D₃	semidirect
373. C₄⋊C₄	C₂×C₃²×D₃	semidirect
419. C₃²	#5634	direct (N × H)
420. C₃²	C₃×#543	semidirect
470. C₃	C₃×#5634	direct (N × H)
471. C₃	C₃²×#543	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₂²⋊Q₈	2
C₃²×#946	2
C₂×C₃²×(C₂×D₃)⋊C₄	2
C₃²×#924	2
C₃²×#897	2
C₃²×#896	2
C₃²×D₃×C₂²⋊C₄	2
C₃²×#878	2
C₃²×#543	3
C₃×#5634	3

Subgroups — C32×#5634 #13179013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5634 #13179013