Subgroups — C₃²×#5555 #13178933

Order 1728.

2128 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#237	C₂	1	2	yes	maximal, complemented
2	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#930	C₂	1	2	yes	maximal, complemented
4	C₂×C₃²×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
5	C₃²×#897	C₂	1	2	yes	maximal, complemented
6	C₃²×#886	C₂	1	4	yes	maximal, complemented
7	C₃²×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#869	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#547	—	3	1	no	maximal
10	C₃×#5555	C₃	1	4	yes	maximal, direct product factor
11	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	C₂²	1	2	yes	—
13	C₂×C₃²×#67	C₂²	1	4	yes	—
14	C₂²×C₃²×Dic₃	C₂²	1	4	yes	—
15	C₃²×#237	—	2	8	no	—
16	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
17	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
18	C₂×C₃²×Dic₆	C₂²	1	2	yes	—
19	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₃³×C₄²	C₂²	1	1	yes	characteristic
22	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
23	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
26	C₃²×C₄⋊Dic₃	C₂²	1	4	yes	—
27	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
28	C₂×C₃²×#41	—	3	2	no	—
29	C₂×C₃×#237	C₂×C₃	1	8	yes	complemented
30	C₃²×C₄⋊Q₈	—	3	1	no	—
31	C₃²×#123	—	3	4	no	—
32	C₃²×C₂²⋊Q₈	—	3	2	no	—
33	C₃²×#121	—	3	2	no	—
34	C₃²×C₄×D₄	—	2	4	no	—
35	C₃²×C₄×D₄	—	3	1	no	—
36	C₃²×C₄×D₄	D₃	1	1	yes	characteristic, complemented
37	C₃²×C₄×D₄	C₂×C₃	1	4	yes	complemented
38	C₂×C₃²×C₄⋊C₄	—	3	2	no	—
39	C₃×#930	C₂×C₃	1	8	yes	complemented
40	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	8	yes	complemented
41	C₃×#897	C₂×C₃	1	8	yes	complemented
42	C₃×#886	C₂×C₃	1	16	yes	complemented
43	C₃×C₄×D₁₂	C₂×C₃	1	4	yes	complemented
44	C₃×#869	C₂×C₃	1	4	yes	complemented
45	C₂³×C₃³	C₂³	1	2	yes	—
46	C₂²×C₃²×D₃	C₂³	1	2	yes	—
47	C₃³×D₄	D₄	1	4	yes	complemented
48	C₂×C₃³×C₄	—	2	4	no	—
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	2	yes	—
51	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
52	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
53	C₃²×#67	—	2	8	no	—
54	C₂×C₃²×Dic₃	—	2	8	no	—
55	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
56	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
57	C₃²×D₁₂	—	2	2	no	—
58	C₃²×C₄×D₃	—	2	4	no	—
59	C₃²×Dic₆	—	2	4	no	—
60	C₃×#547	—	3	4	no	—
61	#5555	C₃²	1	1	yes	characteristic, direct product factor
62	C₃²×#41	—	6	8	no	—
63	C₂×C₃²×Q₈	—	3	2	no	—
64	C₂×C₃²×D₄	—	2	4	no	—
65	C₂×C₃²×D₄	—	3	4	no	—
66	C₂×C₃²×D₄	—	3	1	no	—
67	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
68	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
69	C₂²×C₃²×C₄	—	2	8	no	—
70	C₂²×C₃²×C₄	—	3	4	no	—
71	C₂²×C₃²×C₄	—	3	2	no	—
72	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	—
73	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	—
74	C₂×C₃×#67	C₂²×C₃	1	16	yes	—
75	C₂²×C₃×Dic₃	C₂²×C₃	1	16	yes	—
76	C₃×#237	—	2	32	no	—
77	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
78	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
79	C₂×C₃×Dic₆	C₂²×C₃	1	8	yes	—
80	C₃²×C₄⋊C₄	—	2	4	no	—
81	C₃²×C₄⋊C₄	—	3	1	no	—
82	C₃²×C₄⋊C₄	—	3	2	no	—
83	C₃²×C₄⋊C₄	—	3	4	no	—
84	C₃²×C₄⋊C₄	—	3	2	no	—
85	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
87	C₃²×C₂²⋊C₄	—	2	8	no	—
88	C₃²×C₂²⋊C₄	—	3	2	no	—
89	C₃²×C₂²⋊C₄	—	3	4	no	—
90	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
91	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
92	C₃²×C₄²	—	2	4	no	—
93	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
94	C₃²×C₄²	C₂²×C₃	1	4	yes	—
95	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
96	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	—
97	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
98	C₃×C₄⋊Dic₃	C₂²×C₃	1	16	yes	—
99	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
100	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
101	C₂²×C₃³	—	2	2	no	—
102	C₂²×C₃³	—	2	2	no	—
103	C₂²×C₃³	C₂×D₄	1	4	yes	—
104	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
105	C₂×C₃²×D₃	—	2	2	no	—
106	C₂×C₃²×D₃	—	2	2	no	—
107	C₂×C₃²×D₃	—	2	2	no	—
108	C₃³×C₄	—	2	2	no	—
109	C₃³×C₄	—	2	1	no	—
110	C₃³×C₄	C₂×D₄	1	2	yes	—
111	C₃³×C₄	#41	1	2	yes	complemented
112	C₃²×Dic₃	—	2	4	no	—
113	C₃²×Dic₃	—	2	2	no	—
114	C₂×C₃×#41	—	3	8	no	—
115	C₂×#237	C₂×C₃²	1	2	yes	complemented
116	C₃×C₄⋊Q₈	—	3	4	no	—
117	C₃×#123	—	3	16	no	—
118	C₃×C₂²⋊Q₈	—	3	8	no	—
119	C₃×#121	—	3	8	no	—
120	C₃×C₄×D₄	—	2	4	no	—
121	C₃×C₄×D₄	—	3	4	no	—
122	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
123	C₃×C₄×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
124	C₂×C₃×C₄⋊C₄	—	3	8	no	—
125	#930	C₂×C₃²	1	2	yes	complemented
126	C₂×C₄⋊Dic₃	C₂×C₃²	1	2	yes	complemented
127	#897	C₂×C₃²	1	2	yes	complemented
128	#886	C₂×C₃²	1	4	yes	complemented
129	C₄×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
130	#869	C₂×C₃²	1	1	yes	characteristic, complemented
131	C₂³×C₃²	—	2	8	no	—
132	C₂³×C₃²	—	3	2	no	—
133	C₂³×C₃²	C₂²×D₃	1	2	yes	—
134	C₂³×C₃²	C₂³×C₃	1	8	yes	—
135	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
136	C₃²×Q₈	—	6	4	no	—
137	C₃²×D₄	—	2	16	no	—
138	C₃²×D₄	—	6	8	no	—
139	C₃²×D₄	—	6	2	no	—
140	C₃²×D₄	D₁₂	1	4	yes	complemented
141	C₃²×D₄	C₃×D₄	1	16	yes	complemented
142	C₂×C₃²×C₄	—	2	4	no	—
143	C₂×C₃²×C₄	—	2	4	no	—
144	C₂×C₃²×C₄	—	2	4	no	—
145	C₂×C₃²×C₄	—	2	4	no	—
146	C₂×C₃²×C₄	—	2	8	no	—
147	C₂×C₃²×C₄	—	2	16	no	—
148	C₂×C₃²×C₄	—	3	2	no	—
149	C₂×C₃²×C₄	—	3	4	no	—
150	C₂×C₃²×C₄	—	4	16	no	—
151	C₂×C₃²×C₄	—	6	8	no	—
152	C₂×C₃²×C₄	—	6	4	no	—
153	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
154	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
155	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
156	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
158	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
159	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
160	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
161	C₃×#67	—	2	32	no	—
162	C₂×C₃×Dic₃	—	2	32	no	—
163	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
164	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
165	C₃×D₁₂	—	2	8	no	—
166	C₃×C₄×D₃	—	2	16	no	—
167	C₃×Dic₆	—	2	16	no	—
168	#547	—	3	1	no	Sylow
169	C₂×C₃³	—	2	4	no	—
170	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₃³	C₂×#41	1	1	yes	characteristic
172	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
173	C₃²×D₃	—	4	2	no	—
174	C₃×#41	—	6	32	no	—
175	C₂×C₃×Q₈	—	3	8	no	—
176	C₂×C₃×D₄	—	2	4	no	—
177	C₂×C₃×D₄	—	3	16	no	—
178	C₂×C₃×D₄	—	3	4	no	—
179	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
180	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
181	C₂²×C₃×C₄	—	2	8	no	—
182	C₂²×C₃×C₄	—	3	16	no	—
183	C₂²×C₃×C₄	—	3	8	no	—
184	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
185	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
186	C₂×#67	C₂²×C₃²	1	4	yes	—
187	C₂²×Dic₃	C₂²×C₃²	1	4	yes	—
188	#237	—	2	8	no	—
189	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
190	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
191	C₂×Dic₆	C₂²×C₃²	1	2	yes	—
192	C₃×C₄⋊C₄	—	2	4	no	—
193	C₃×C₄⋊C₄	—	3	4	no	—
194	C₃×C₄⋊C₄	—	3	8	no	—
195	C₃×C₄⋊C₄	—	3	16	no	—
196	C₃×C₄⋊C₄	—	3	8	no	—
197	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
198	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	—	2	8	no	—
200	C₃×C₂²⋊C₄	—	3	8	no	—
201	C₃×C₂²⋊C₄	—	3	16	no	—
202	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
203	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
204	C₃×C₄²	—	2	4	no	—
205	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
206	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
207	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
208	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	—
209	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
210	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
211	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
212	C₄⋊Dic₃	C₂²×C₃²	1	4	yes	—
213	C₂²×C₃²	—	2	2	no	—
214	C₂²×C₃²	—	2	2	no	—
215	C₂²×C₃²	—	2	4	no	—
216	C₂²×C₃²	—	2	16	no	—
217	C₂²×C₃²	—	2	8	no	—
218	C₂²×C₃²	—	2	8	no	—
219	C₂²×C₃²	—	4	8	no	—
220	C₂²×C₃²	—	4	8	no	—
221	C₂²×C₃²	—	6	2	no	—
222	C₂²×C₃²	—	6	2	no	—
223	C₂²×C₃²	—	6	2	no	—
224	C₂²×C₃²	C₂×D₁₂	1	4	yes	—
225	C₂²×C₃²	C₂×C₃×D₄	1	16	yes	—
226	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
227	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
228	C₂×C₃×D₃	—	2	8	no	—
229	C₂×C₃×D₃	—	2	8	no	—
230	C₂×C₃×D₃	—	2	8	no	—
231	C₃²×C₄	—	2	2	no	—
232	C₃²×C₄	—	2	1	no	—
233	C₃²×C₄	—	2	8	no	—
234	C₃²×C₄	—	2	8	no	—
235	C₃²×C₄	—	2	8	no	—
236	C₃²×C₄	—	2	4	no	—
237	C₃²×C₄	—	4	4	no	—
238	C₃²×C₄	—	4	8	no	—
239	C₃²×C₄	—	6	2	no	—
240	C₃²×C₄	—	6	4	no	—
241	C₃²×C₄	C₂×D₁₂	1	2	yes	—
242	C₃²×C₄	#237	1	2	yes	complemented
243	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
244	C₃²×C₄	C₃×#41	1	8	yes	complemented
245	C₃×Dic₃	—	2	16	no	—
246	C₃×Dic₃	—	2	8	no	—
247	C₂×#41	—	3	2	no	—
248	C₄⋊Q₈	—	3	1	no	—
249	#123	—	3	4	no	—
250	C₂²⋊Q₈	—	3	2	no	—
251	#121	—	3	2	no	—
252	C₄×D₄	—	3	1	no	—
253	C₄×D₄	C₃²×D₃	1	1	yes	characteristic, complemented
254	C₂×C₄⋊C₄	—	3	2	no	—
255	C₃³	#547	1	1	yes	characteristic, complemented, Sylow
256	C₂³×C₃	—	2	8	no	—
257	C₂³×C₃	—	3	8	no	—
258	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
259	C₂³×C₃	C₂³×C₃²	1	2	yes	—
260	C₂²×D₃	C₂³×C₃²	1	2	yes	—
261	C₃×Q₈	—	6	16	no	—
262	C₃×D₄	—	2	16	no	—
263	C₃×D₄	—	6	32	no	—
264	C₃×D₄	—	6	8	no	—
265	C₃×D₄	C₃×D₁₂	1	16	yes	complemented
266	C₃×D₄	C₃²×D₄	1	4	yes	complemented
267	C₂×C₃×C₄	—	2	16	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	3	8	no	—
274	C₂×C₃×C₄	—	3	16	no	—
275	C₂×C₃×C₄	—	4	16	no	—
276	C₂×C₃×C₄	—	6	32	no	—
277	C₂×C₃×C₄	—	6	16	no	—
278	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
279	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
280	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
281	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
282	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
284	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
286	#67	—	2	8	no	—
287	C₂×Dic₃	—	2	8	no	—
288	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
289	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
290	D₁₂	—	2	2	no	—
291	C₄×D₃	—	2	4	no	—
292	Dic₆	—	2	4	no	—
293	C₂×C₃²	—	2	4	no	—
294	C₂×C₃²	—	2	4	no	—
295	C₂×C₃²	—	2	4	no	—
296	C₂×C₃²	—	2	4	no	—
297	C₂×C₃²	—	2	16	no	—
298	C₂×C₃²	—	4	16	no	—
299	C₂×C₃²	—	12	2	no	—
300	C₂×C₃²	C₂²×D₁₂	1	1	yes	characteristic
301	C₂×C₃²	C₂×#237	1	1	yes	characteristic
302	C₂×C₃²	#1010	1	1	yes	characteristic
303	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
304	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
305	C₂×C₃²	C₃×2₋¹⁺⁴	1	4	yes	—
306	C₃×D₃	—	4	8	no	—
307	#41	—	6	8	no	—
308	C₂×Q₈	—	3	2	no	—
309	C₂×D₄	—	3	4	no	—
310	C₂×D₄	—	3	1	no	—
311	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
312	C₂²×C₄	—	3	4	no	—
313	C₂²×C₄	—	3	2	no	—
314	C₂²×C₄	C₂×C₃²×D₃	1	2	yes	—
315	C₄⋊C₄	—	3	1	no	—
316	C₄⋊C₄	—	3	2	no	—
317	C₄⋊C₄	—	3	4	no	—
318	C₄⋊C₄	—	3	2	no	—
319	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
320	C₂²⋊C₄	—	3	2	no	—
321	C₂²⋊C₄	—	3	4	no	—
322	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	—
323	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
324	C₂²×C₃	—	2	8	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	16	no	—
330	C₂²×C₃	—	4	8	no	—
331	C₂²×C₃	—	4	8	no	—
332	C₂²×C₃	—	6	8	no	—
333	C₂²×C₃	—	6	8	no	—
334	C₂²×C₃	—	6	8	no	—
335	C₂²×C₃	C₂×C₃×D₁₂	1	16	yes	—
336	C₂²×C₃	C₂×C₃²×D₄	1	4	yes	—
337	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
338	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
339	C₂×D₃	—	2	2	no	—
340	C₂×D₃	—	2	2	no	—
341	C₂×D₃	—	2	2	no	—
342	C₃×C₄	—	2	8	no	—
343	C₃×C₄	—	2	4	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	8	no	—
347	C₃×C₄	—	2	8	no	—
348	C₃×C₄	—	4	8	no	—
349	C₃×C₄	—	4	4	no	—
350	C₃×C₄	—	6	8	no	—
351	C₃×C₄	—	6	16	no	—
352	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	—
353	C₃×C₄	C₃×#237	1	8	yes	complemented
354	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
355	C₃×C₄	C₃²×#41	1	2	yes	complemented
356	Dic₃	—	2	4	no	—
357	Dic₃	—	2	2	no	—
358	C₃²	—	2	4	no	—
359	C₃²	#5555	1	1	yes	characteristic, direct product factor
360	C₃²	C₃×#547	1	4	yes	complemented
361	C₂³	—	3	2	no	—
362	C₂³	C₂²×C₃²×D₃	1	2	yes	—
363	Q₈	—	6	4	no	—
364	D₄	—	6	8	no	—
365	D₄	—	6	2	no	—
366	D₄	C₃²×D₁₂	1	4	yes	complemented
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	3	2	no	—
369	C₂×C₄	—	3	4	no	—
370	C₂×C₄	—	6	8	no	—
371	C₂×C₄	—	6	4	no	—
372	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
374	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
376	C₂×C₃	—	2	16	no	—
377	C₂×C₃	—	2	4	no	—
378	C₂×C₃	—	2	4	no	—
379	C₂×C₃	—	2	4	no	—
380	C₂×C₃	—	2	4	no	—
381	C₂×C₃	—	4	16	no	—
382	C₂×C₃	—	12	8	no	—
383	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
384	C₂×C₃	C₂×C₃×#237	1	4	yes	—
385	C₂×C₃	C₃×#1010	1	4	yes	—
386	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
387	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
388	C₂×C₃	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
389	D₃	—	4	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	6	2	no	—
393	C₂²	—	6	2	no	—
394	C₂²	—	6	2	no	—
395	C₂²	C₂×C₃²×D₁₂	1	4	yes	—
396	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	6	2	no	—
400	C₄	—	6	4	no	—
401	C₄	C₂×C₃²×D₁₂	1	2	yes	—
402	C₄	C₃²×#237	1	2	yes	complemented
403	C₃	—	2	4	no	—
404	C₃	C₃×#5555	1	4	yes	direct product factor
405	C₃	C₃²×#547	1	1	yes	characteristic, complemented
406	C₂	—	2	4	no	—
407	C₂	—	12	2	no	—
408	C₂	C₂²×C₃²×D₁₂	1	1	yes	characteristic
409	C₂	C₂×C₃²×#237	1	1	yes	characteristic
410	C₂	C₃²×#1010	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×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃²×C₄×D₄	D₃
hypocenter	C₃	C₃²×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#237	C₂	semidirect
2. C₃³×C₄×D₄	C₂	semidirect
3. C₃²×#930	C₂	semidirect
4. C₂×C₃²×C₄⋊Dic₃	C₂	semidirect
5. C₃²×#897	C₂	semidirect
6. C₃²×#886	C₂	semidirect
7. C₃²×C₄×D₁₂	C₂	semidirect
8. C₃²×#869	C₂	semidirect
10. C₃×#5555	C₃	direct (N × H)
29. C₂×C₃×#237	C₂×C₃	semidirect
36. C₃²×C₄×D₄	D₃	semidirect
37. C₃²×C₄×D₄	C₂×C₃	semidirect
39. C₃×#930	C₂×C₃	semidirect
40. C₂×C₃×C₄⋊Dic₃	C₂×C₃	semidirect
41. C₃×#897	C₂×C₃	semidirect
42. C₃×#886	C₂×C₃	semidirect
43. C₃×C₄×D₁₂	C₂×C₃	semidirect
44. C₃×#869	C₂×C₃	semidirect
47. C₃³×D₄	D₄	semidirect
61. #5555	C₃²	direct (N × H)
111. C₃³×C₄	#41	semidirect
115. C₂×#237	C₂×C₃²	semidirect
122. C₃×C₄×D₄	C₃×D₃	semidirect
123. C₃×C₄×D₄	C₂×C₃²	semidirect
125. #930	C₂×C₃²	semidirect
126. C₂×C₄⋊Dic₃	C₂×C₃²	semidirect
127. #897	C₂×C₃²	semidirect
128. #886	C₂×C₃²	semidirect
129. C₄×D₁₂	C₂×C₃²	semidirect
130. #869	C₂×C₃²	semidirect
140. C₃²×D₄	D₁₂	semidirect
141. C₃²×D₄	C₃×D₄	semidirect
242. C₃²×C₄	#237	semidirect
244. C₃²×C₄	C₃×#41	semidirect
253. C₄×D₄	C₃²×D₃	semidirect
255. C₃³	#547	semidirect
265. C₃×D₄	C₃×D₁₂	semidirect
266. C₃×D₄	C₃²×D₄	semidirect
353. C₃×C₄	C₃×#237	semidirect
355. C₃×C₄	C₃²×#41	semidirect
359. C₃²	#5555	direct (N × H)
360. C₃²	C₃×#547	semidirect
366. D₄	C₃²×D₁₂	semidirect
402. C₄	C₃²×#237	semidirect
404. C₃	C₃×#5555	direct (N × H)
405. C₃	C₃²×#547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#237	2
C₃³×C₄×D₄	2
C₃²×#930	2
C₂×C₃²×C₄⋊Dic₃	2
C₃²×#897	2
C₃²×#886	2
C₃²×C₄×D₁₂	2
C₃²×#869	2
C₃²×#547	3
C₃×#5555	3

Subgroups — C32×#5555 #13178933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5555 #13178933