Subgroups — #13179740

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	#11723980	C₂	1	1	yes	maximal, characteristic, complemented
3	#11723979	C₂	1	1	yes	maximal, characteristic, complemented
4	#11723978	C₂	1	1	yes	maximal, characteristic, complemented
5	#11723978	C₂	1	1	yes	maximal, characteristic, complemented
6	#11723977	C₂	1	1	yes	maximal, characteristic, complemented
7	#11723976	C₂	1	1	yes	maximal, characteristic, complemented
8	#11723970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#6312	C₂	1	1	yes	maximal, characteristic, complemented
10	#11723939	C₂	1	1	yes	maximal, characteristic, complemented
11	#11723937	C₂	1	1	yes	maximal, characteristic, complemented
12	#11723926	C₂	1	1	yes	maximal, characteristic, complemented
13	#11723922	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
15	#11723920	C₂	1	1	yes	maximal, characteristic, complemented
16	#10596084	—	3	13	no	maximal
17	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
18	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×#6312	C₂²	1	1	yes	characteristic
23	C₂×#6312	C₂²	1	1	yes	characteristic
24	C₂×#6312	C₂²	1	1	yes	characteristic
25	C₂×#6312	C₂²	1	1	yes	characteristic
26	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
29	C₂×#6308	C₂²	1	1	yes	characteristic, complemented
30	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	#88864	C₂²	1	1	yes	characteristic
34	#88864	C₂²	1	1	yes	characteristic
35	#88864	C₂²	1	1	yes	characteristic
36	#88864	C₂²	1	1	yes	characteristic, complemented
37	#88864	C₂²	1	1	yes	characteristic, complemented
38	#88864	C₂²	1	1	yes	characteristic, complemented
39	#88859	C₂²	1	1	yes	characteristic
40	#88859	C₂²	1	1	yes	characteristic
41	#88859	C₂²	1	1	yes	characteristic
42	#88859	C₂²	1	1	yes	characteristic
43	#88859	C₂²	1	1	yes	characteristic
44	#88859	C₂²	1	1	yes	characteristic
45	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic, complemented
46	#88857	C₂²	1	1	yes	characteristic, complemented
47	#88857	C₂²	1	1	yes	characteristic, complemented
48	#88857	C₂²	1	1	yes	characteristic, complemented
49	#88857	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
52	C₃²×#121	D₃	1	13	yes	complemented
53	#64148	—	3	13	no	—
54	#64147	—	3	13	no	—
55	#64146	—	3	13	no	—
56	#64146	—	3	13	no	—
57	#64145	—	3	13	no	—
58	#64144	—	3	13	no	—
59	#64138	—	3	13	no	—
60	C₄×#638	—	3	13	no	—
61	#64107	—	3	13	no	—
62	#64105	—	3	13	no	—
63	#64094	—	3	13	no	—
64	#64090	—	3	13	no	—
65	C₂²⋊C₄×C₃⋊D₃	—	3	13	no	—
66	#64088	—	3	13	no	—
67	C₂³×C₃³	C₂³	1	1	yes	characteristic
68	C₂³×C₃³	C₂³	1	1	yes	characteristic
69	C₂³×C₃³	C₂³	1	1	yes	characteristic
70	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
71	C₂²×C₃⋊(C₃⋊D₃)	—	4	1	no	—
72	C₂²×C₃⋊(C₃⋊D₃)	—	4	1	no	—
73	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
74	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
75	C₃³×D₄	—	4	1	no	—
76	C₃³×D₄	—	4	1	no	—
77	C₃³×D₄	—	4	1	no	—
78	C₂×C₃³×C₄	—	4	1	no	—
79	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
80	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
81	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
82	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
83	#6312	—	2	2	no	—
84	#6312	—	2	2	no	—
85	#6312	—	4	1	no	—
86	#6312	—	4	1	no	—
87	C₂×C₃⋊(C₃⋊Dic₃)	—	4	1	no	—
88	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
89	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
90	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
91	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
92	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
93	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
94	C₄×C₃⋊(C₃⋊D₃)	—	4	1	no	—
95	C₄×C₃⋊(C₃⋊D₃)	—	4	1	no	—
96	#6308	—	4	1	no	—
97	#5613	—	9	13	no	—
98	C₂³×C₃⋊D₃	—	3	13	no	—
99	C₂×C₃²×D₄	C₂×D₃	1	13	yes	—
100	C₂×C₃²×D₄	C₂×D₃	1	13	yes	—
101	C₂×C₃²×D₄	C₂×D₃	1	13	yes	complemented
102	C₂²×C₃²×C₄	C₂×D₃	1	13	yes	complemented
103	C₂×#638	—	3	13	no	—
104	C₂×#638	—	3	13	no	—
105	C₂×#638	—	3	13	no	—
106	C₂×#638	—	3	13	no	—
107	C₂²×C₃⋊Dic₃	—	3	13	no	—
108	C₂×C₄×C₃⋊D₃	—	3	13	no	—
109	C₂×C₄×C₃⋊D₃	—	3	13	no	—
110	C₂×#634	—	3	13	no	—
111	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	complemented
112	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	—
113	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	complemented
114	#3757	—	3	13	no	—
115	#3757	—	3	13	no	—
116	#3757	—	3	13	no	—
117	#3757	—	3	13	no	—
118	#3757	—	3	13	no	—
119	#3757	—	3	13	no	—
120	#3752	—	3	13	no	—
121	#3752	—	3	13	no	—
122	#3752	—	3	13	no	—
123	#3752	—	3	13	no	—
124	#3752	—	3	13	no	—
125	#3752	—	3	13	no	—
126	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
127	#3750	—	3	13	no	—
128	#3750	—	3	13	no	—
129	#3750	—	3	13	no	—
130	#3750	—	3	13	no	—
131	C₄×C₃⋊Dic₃	—	3	13	no	—
132	C₄×C₃⋊Dic₃	—	3	13	no	—
133	C₂²×C₃³	—	2	1	no	—
134	C₂²×C₃³	—	2	1	no	—
135	C₂²×C₃³	—	2	1	no	—
136	C₂²×C₃³	—	2	1	no	—
137	C₂²×C₃³	—	2	1	no	—
138	C₂²×C₃³	—	2	1	no	—
139	C₂²×C₃³	—	2	1	no	—
140	C₂²×C₃³	—	2	1	no	—
141	C₂²×C₃³	—	2	1	no	—
142	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
143	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
144	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
145	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
146	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
147	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
148	C₂×C₃⋊(C₃⋊D₃)	—	4	4	no	—
149	C₂×C₃⋊(C₃⋊D₃)	#41	1	2	yes	—
150	C₃³×C₄	—	2	1	no	—
151	C₃³×C₄	—	2	1	no	—
152	C₃³×C₄	—	2	1	no	—
153	C₃³×C₄	—	2	1	no	—
154	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
155	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
156	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
157	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
158	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
159	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
160	C₃×#121	C₃⋊D₃	1	13	yes	complemented
161	#939	—	9	13	no	—
162	#938	—	9	13	no	—
163	#937	—	9	13	no	—
164	#937	—	9	13	no	—
165	#936	—	9	13	no	—
166	#935	—	9	13	no	—
167	#929	—	9	13	no	—
168	C₄×#67	—	9	13	no	—
169	#898	—	9	13	no	—
170	#896	—	9	13	no	—
171	#885	—	9	13	no	—
172	#67⋊C₄	—	9	13	no	—
173	D₃×C₂²⋊C₄	—	9	13	no	—
174	#879	—	9	13	no	—
175	C₂³×C₃²	C₂²×D₃	1	13	yes	—
176	C₂³×C₃²	C₂²×D₃	1	13	yes	—
177	C₂³×C₃²	C₂²×D₃	1	13	yes	—
178	C₂²×C₃⋊D₃	—	3	13	no	—
179	C₂²×C₃⋊D₃	—	3	13	no	—
180	C₂²×C₃⋊D₃	—	6	26	no	—
181	C₂²×C₃⋊D₃	—	12	13	no	—
182	C₂²×C₃⋊D₃	—	12	13	no	—
183	C₃²×D₄	—	4	13	no	—
184	C₃²×D₄	—	4	13	no	—
185	C₃²×D₄	—	4	13	no	—
186	C₂×C₃²×C₄	—	4	13	no	—
187	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
188	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
189	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
190	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
191	#638	—	6	26	no	—
192	#638	—	6	26	no	—
193	#638	—	12	13	no	—
194	#638	—	12	13	no	—
195	C₂×C₃⋊Dic₃	—	3	13	no	—
196	C₂×C₃⋊Dic₃	—	3	13	no	—
197	C₂×C₃⋊Dic₃	—	3	13	no	—
198	C₂×C₃⋊Dic₃	—	3	13	no	—
199	C₂×C₃⋊Dic₃	—	3	13	no	—
200	C₂×C₃⋊Dic₃	—	3	13	no	—
201	C₂×C₃⋊Dic₃	—	12	13	no	—
202	C₄×C₃⋊D₃	—	12	13	no	—
203	C₄×C₃⋊D₃	—	12	13	no	—
204	#634	—	12	13	no	—
205	#538	—	27	1	no	Sylow
206	C₂×C₃³	—	4	1	no	—
207	C₂×C₃³	—	4	1	no	—
208	C₂×C₃³	—	4	1	no	—
209	C₂×C₃³	C₂×#41	1	1	yes	characteristic
210	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
212	C₃⋊(C₃⋊D₃)	—	2	2	no	—
213	C₃⋊(C₃⋊D₃)	—	4	1	no	—
214	C₂³×D₃	—	9	13	no	—
215	C₂×C₃×D₄	C₂×C₃⋊D₃	1	13	yes	—
216	C₂×C₃×D₄	C₂×C₃⋊D₃	1	13	yes	—
217	C₂×C₃×D₄	C₂×C₃⋊D₃	1	13	yes	complemented
218	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	13	yes	complemented
219	C₂×#67	—	9	13	no	—
220	C₂×#67	—	9	13	no	—
221	C₂×#67	—	9	13	no	—
222	C₂×#67	—	9	13	no	—
223	C₂²×Dic₃	—	9	13	no	—
224	C₂×C₄×D₃	—	9	13	no	—
225	C₂×C₄×D₃	—	9	13	no	—
226	C₂×Dic₆	—	9	13	no	—
227	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
228	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
229	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
230	#217	—	9	13	no	—
231	#217	—	9	13	no	—
232	#217	—	9	13	no	—
233	#217	—	9	13	no	—
234	#217	—	9	13	no	—
235	#217	—	9	13	no	—
236	(C₂×D₃)⋊C₄	—	9	13	no	—
237	(C₂×D₃)⋊C₄	—	9	13	no	—
238	(C₂×D₃)⋊C₄	—	9	13	no	—
239	(C₂×D₃)⋊C₄	—	9	13	no	—
240	(C₂×D₃)⋊C₄	—	9	13	no	—
241	(C₂×D₃)⋊C₄	—	9	13	no	—
242	C₄⋊Dic₃	—	9	13	no	—
243	Dic₃⋊C₄	—	9	13	no	—
244	Dic₃⋊C₄	—	9	13	no	—
245	Dic₃⋊C₄	—	9	13	no	—
246	Dic₃⋊C₄	—	9	13	no	—
247	C₄×Dic₃	—	9	13	no	—
248	C₄×Dic₃	—	9	13	no	—
249	C₂²×C₃²	—	2	13	no	—
250	C₂²×C₃²	—	2	13	no	—
251	C₂²×C₃²	—	2	13	no	—
252	C₂²×C₃²	—	2	13	no	—
253	C₂²×C₃²	—	2	13	no	—
254	C₂²×C₃²	—	2	13	no	—
255	C₂²×C₃²	—	2	13	no	—
256	C₂²×C₃²	—	2	13	no	—
257	C₂²×C₃²	—	2	13	no	—
258	C₂²×C₃²	C₂³×D₃	1	13	yes	—
259	C₂×C₃⋊D₃	—	3	26	no	—
260	C₂×C₃⋊D₃	—	6	13	no	—
261	C₂×C₃⋊D₃	—	6	13	no	—
262	C₂×C₃⋊D₃	—	6	13	no	—
263	C₂×C₃⋊D₃	—	6	13	no	—
264	C₂×C₃⋊D₃	—	6	13	no	—
265	C₂×C₃⋊D₃	—	12	52	no	—
266	C₃²×C₄	—	2	13	no	—
267	C₃²×C₄	—	2	13	no	—
268	C₃²×C₄	—	2	13	no	—
269	C₃²×C₄	—	2	13	no	—
270	C₃⋊Dic₃	—	6	13	no	—
271	C₃⋊Dic₃	—	6	13	no	—
272	C₃⋊Dic₃	—	6	13	no	—
273	C₃⋊Dic₃	—	6	13	no	—
274	C₃⋊Dic₃	—	6	13	no	—
275	C₃⋊Dic₃	—	6	13	no	—
276	#126	—	27	1	no	—
277	#126	—	27	1	no	—
278	#124	—	27	1	no	—
279	#124	—	27	1	no	—
280	#123	—	27	1	no	—
281	#123	—	27	1	no	—
282	C₂²⋊Q₈	—	27	1	no	—
283	#121	—	27	1	no	—
284	#121	—	27	1	no	—
285	#121	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
286	#120	—	27	1	no	—
287	#120	—	27	1	no	—
288	C₄×D₄	—	27	1	no	—
289	C₄×D₄	—	27	1	no	—
290	C₂×C₂²⋊C₄	—	27	1	no	—
291	C₃³	#538	1	1	yes	characteristic, complemented, Sylow
292	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
293	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
294	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
295	C₂²×D₃	—	9	13	no	—
296	C₂²×D₃	—	9	13	no	—
297	C₂²×D₃	—	18	26	no	—
298	C₂²×D₃	—	36	13	no	—
299	C₂²×D₃	—	36	13	no	—
300	C₃×D₄	—	4	13	no	—
301	C₃×D₄	—	4	13	no	—
302	C₃×D₄	—	4	13	no	—
303	C₂×C₃×C₄	—	4	13	no	—
304	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
305	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
306	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
307	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
308	#67	—	18	26	no	—
309	#67	—	18	26	no	—
310	#67	—	36	13	no	—
311	#67	—	36	13	no	—
312	C₂×Dic₃	—	9	13	no	—
313	C₂×Dic₃	—	9	13	no	—
314	C₂×Dic₃	—	9	13	no	—
315	C₂×Dic₃	—	9	13	no	—
316	C₂×Dic₃	—	9	13	no	—
317	C₂×Dic₃	—	9	13	no	—
318	C₂×Dic₃	—	36	13	no	—
319	C₄×D₃	—	36	13	no	—
320	C₄×D₃	—	36	13	no	—
321	Dic₆	—	36	13	no	—
322	C₂×C₃²	—	4	13	no	—
323	C₂×C₃²	—	4	13	no	—
324	C₂×C₃²	—	4	13	no	—
325	C₂×C₃²	#1004	1	13	yes	—
326	C₂×C₃²	#1004	1	13	yes	—
327	C₂×C₃²	D₃×#41	1	13	yes	—
328	C₃⋊D₃	—	6	26	no	—
329	C₃⋊D₃	—	12	13	no	—
330	C₂⁴	—	27	1	no	—
331	C₂×Q₈	—	27	1	no	—
332	C₂×D₄	—	27	1	no	—
333	C₂×D₄	—	27	1	no	—
334	C₂×D₄	—	27	1	no	—
335	C₂×D₄	—	27	1	no	—
336	C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
337	C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
338	C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
339	C₂²×C₄	—	27	1	no	—
340	C₂²×C₄	—	27	1	no	—
341	C₂²×C₄	—	27	1	no	—
342	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
343	C₄⋊C₄	—	27	1	no	—
344	C₄⋊C₄	—	27	1	no	—
345	C₄⋊C₄	—	27	1	no	—
346	C₄⋊C₄	—	27	1	no	—
347	C₄⋊C₄	—	27	1	no	—
348	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
349	C₂²⋊C₄	—	27	1	no	—
350	C₂²⋊C₄	—	27	1	no	—
351	C₂²⋊C₄	—	27	1	no	—
352	C₂²⋊C₄	—	27	1	no	—
353	C₂²⋊C₄	—	27	1	no	—
354	C₂²⋊C₄	—	27	1	no	—
355	C₂²⋊C₄	—	27	1	no	—
356	C₂²⋊C₄	—	27	1	no	—
357	C₂²⋊C₄	—	27	1	no	—
358	C₂²⋊C₄	—	27	1	no	—
359	C₂²⋊C₄	—	27	1	no	—
360	C₂²⋊C₄	—	27	1	no	—
361	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
362	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
363	C₄²	—	27	1	no	—
364	C₄²	—	27	1	no	—
365	C₂²×C₃	—	2	13	no	—
366	C₂²×C₃	—	2	13	no	—
367	C₂²×C₃	—	2	13	no	—
368	C₂²×C₃	—	2	13	no	—
369	C₂²×C₃	—	2	13	no	—
370	C₂²×C₃	—	2	13	no	—
371	C₂²×C₃	—	2	13	no	—
372	C₂²×C₃	—	2	13	no	—
373	C₂²×C₃	—	2	13	no	—
374	C₂²×C₃	C₂³×C₃⋊D₃	1	13	yes	—
375	C₂×D₃	—	9	26	no	—
376	C₂×D₃	—	18	13	no	—
377	C₂×D₃	—	18	13	no	—
378	C₂×D₃	—	18	13	no	—
379	C₂×D₃	—	18	13	no	—
380	C₂×D₃	—	18	13	no	—
381	C₂×D₃	—	36	52	no	—
382	C₃×C₄	—	2	13	no	—
383	C₃×C₄	—	2	13	no	—
384	C₃×C₄	—	2	13	no	—
385	C₃×C₄	—	2	13	no	—
386	Dic₃	—	18	13	no	—
387	Dic₃	—	18	13	no	—
388	Dic₃	—	18	13	no	—
389	Dic₃	—	18	13	no	—
390	Dic₃	—	18	13	no	—
391	Dic₃	—	18	13	no	—
392	C₃²	#5613	1	13	yes	complemented
393	C₂³	—	27	1	no	—
394	C₂³	—	27	1	no	—
395	C₂³	—	54	2	no	—
396	C₂³	—	108	1	no	—
397	C₂³	—	108	1	no	—
398	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
399	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
400	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
401	Q₈	—	108	1	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	4	1	no	—
405	D₄	—	54	2	no	—
406	D₄	—	54	2	no	—
407	D₄	—	108	1	no	—
408	D₄	—	108	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	27	1	no	—
411	C₂×C₄	—	27	1	no	—
412	C₂×C₄	—	27	1	no	—
413	C₂×C₄	—	27	1	no	—
414	C₂×C₄	—	27	1	no	—
415	C₂×C₄	—	27	1	no	—
416	C₂×C₄	—	108	1	no	—
417	C₂×C₄	—	108	1	no	—
418	C₂×C₄	—	108	1	no	—
419	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
423	C₂×C₃	—	4	13	no	—
424	C₂×C₃	—	4	13	no	—
425	C₂×C₃	—	4	13	no	—
426	C₂×C₃	#64361	1	13	yes	—
427	C₂×C₃	#64361	1	13	yes	—
428	C₂×C₃	#41×C₃⋊D₃	1	13	yes	—
429	D₃	—	18	26	no	—
430	D₃	—	36	13	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	27	2	no	—
441	C₂²	—	54	1	no	—
442	C₂²	—	54	1	no	—
443	C₂²	—	54	1	no	—
444	C₂²	—	54	1	no	—
445	C₂²	—	54	1	no	—
446	C₂²	—	108	4	no	—
447	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	54	1	no	—
453	C₄	—	54	1	no	—
454	C₄	—	54	1	no	—
455	C₄	—	54	1	no	—
456	C₄	—	54	1	no	—
457	C₄	—	54	1	no	—
458	C₃	#10596084	1	13	yes	complemented
459	C₂	—	4	1	no	—
460	C₂	—	4	1	no	—
461	C₂	—	4	1	no	—
462	C₂	—	54	2	no	—
463	C₂	—	108	1	no	—
464	C₂	#11724679	1	1	yes	characteristic
465	C₂	#11724679	1	1	yes	characteristic
466	C₂	#41×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
commutator, socle, cosocle	C₂²×C₃³	C₂⁴
Fitting	C₃³×#121	C₂
hypercenter	#121	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#538
LCS	G ▷ C₂²×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ #121

Complements

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

N	H ≅ G/N	type
1. C₃³×#121	C₂	semidirect
2. #11723980	C₂	semidirect
3. #11723979	C₂	semidirect
4. #11723978	C₂	semidirect
5. #11723978	C₂	semidirect
6. #11723977	C₂	semidirect
7. #11723976	C₂	semidirect
8. #11723970	C₂	semidirect
9. C₄×#6312	C₂	semidirect
10. #11723939	C₂	semidirect
11. #11723937	C₂	semidirect
12. #11723926	C₂	semidirect
13. #11723922	C₂	semidirect
14. C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
15. #11723920	C₂	semidirect
20. C₂×C₃³×D₄	C₂²	semidirect
21. C₂²×C₃³×C₄	C₂²	semidirect
26. C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
29. C₂×#6308	C₂²	semidirect
30. C₃³×C₄⋊C₄	C₂²	semidirect
32. C₃³×C₂²⋊C₄	C₂²	semidirect
36. #88864	C₂²	semidirect
37. #88864	C₂²	semidirect
38. #88864	C₂²	semidirect
45. C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	semidirect
46. #88857	C₂²	semidirect
47. #88857	C₂²	semidirect
48. #88857	C₂²	semidirect
49. #88857	C₂²	semidirect
50. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
51. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
52. C₃²×#121	D₃	semidirect
101. C₂×C₃²×D₄	C₂×D₃	semidirect
102. C₂²×C₃²×C₄	C₂×D₃	semidirect
111. C₃²×C₄⋊C₄	C₂×D₃	semidirect
113. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
160. C₃×#121	C₃⋊D₃	semidirect
217. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
218. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
227. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
229. C₃×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
285. #121	C₃⋊(C₃⋊D₃)	semidirect
291. C₃³	#538	semidirect
338. C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
342. C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
348. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
362. C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
392. C₃²	#5613	semidirect
458. C₃	#10596084	semidirect

Maximal subgroups

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

subgroup	index
C₃³×#121	2
#11723980	2
#11723979	2
#11723978	2
#11723977	2
#11723976	2
#11723970	2
C₄×#6312	2
#11723939	2
#11723937	2
#11723926	2
#11723922	2
C₂²⋊C₄×C₃⋊(C₃⋊D₃)	2
#11723920	2
#10596084	3