Subgroups — #13179675

Order 1728.

4620 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#89076	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#11723980	C₂	1	1	yes	maximal, characteristic, complemented
5	#11723978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#6312	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#6312	C₂	1	1	yes	maximal, characteristic, complemented
8	#11723937	C₂	1	1	yes	maximal, characteristic, complemented
9	#11723935	C₂	1	1	yes	maximal, characteristic, complemented
10	#11723925	C₂	1	1	yes	maximal, characteristic, complemented
11	#11723924	C₂	1	1	yes	maximal, characteristic, complemented
12	#11723923	C₂	1	1	yes	maximal, characteristic, complemented
13	#11723919	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic, complemented
15	#11723913	C₂	1	1	yes	maximal, characteristic, complemented
16	#10596018	—	3	13	no	maximal
17	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
18	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
21	C₂×#6312	C₂²	1	1	yes	characteristic
22	C₂×#6312	C₂²	1	1	yes	characteristic
23	C₂×#6312	C₂²	1	1	yes	characteristic
24	C₂×#6312	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
26	#89076	—	2	4	no	—
27	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₃⋊(C₃⋊D₃)	—	2	4	no	—
30	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
35	C₂×#6308	C₂²	1	1	yes	characteristic, complemented
36	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
40	#88864	C₂²	1	1	yes	characteristic
41	#88864	C₂²	1	1	yes	characteristic, complemented
42	#88859	C₂²	1	1	yes	characteristic
43	#88859	C₂²	1	1	yes	characteristic
44	#88859	C₂²	1	1	yes	characteristic
45	#88859	C₂²	1	1	yes	characteristic
46	#88859	C₂²	1	1	yes	characteristic, complemented
47	#88859	C₂²	1	1	yes	characteristic, complemented
48	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic, complemented
49	#88857	C₂²	1	1	yes	characteristic, complemented
50	#88857	C₂²	1	1	yes	characteristic, complemented
51	#88857	C₂²	1	1	yes	characteristic, complemented
52	#88857	C₂²	1	1	yes	characteristic, complemented
53	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
54	C₂×#3828	—	3	13	no	—
55	C₂²×C₄×C₃⋊D₃	—	3	13	no	—
56	C₃²×C₄×D₄	D₃	1	13	yes	complemented
57	#64148	—	3	13	no	—
58	#64146	—	3	13	no	—
59	C₄×#638	—	3	13	no	—
60	C₄×#638	—	3	13	no	—
61	#64105	—	3	13	no	—
62	#64103	—	3	13	no	—
63	#64093	—	3	13	no	—
64	#64092	—	3	13	no	—
65	#64091	—	3	13	no	—
66	#64087	—	3	13	no	—
67	C₄×C₄⋊(C₃⋊D₃)	—	3	13	no	—
68	#64081	—	3	13	no	—
69	C₂³×C₃³	C₂³	1	1	yes	characteristic
70	C₂³×C₃³	C₂³	1	1	yes	characteristic
71	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
72	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
73	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
74	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
75	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
76	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
77	C₃³×D₄	—	2	2	no	—
78	C₂×C₃³×C₄	—	2	2	no	—
79	C₂×C₃³×C₄	—	2	2	no	—
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	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
84	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
85	#6312	—	2	2	no	—
86	#6312	—	2	2	no	—
87	#6312	—	2	2	no	—
88	#6312	—	2	2	no	—
89	C₂×C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
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	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
95	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
96	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
97	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
98	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
99	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
100	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
101	C₄×C₃⋊(C₃⋊D₃)	D₄	1	4	yes	complemented
102	#6308	—	2	2	no	—
103	#5547	—	9	13	no	—
104	C₂³×C₃⋊D₃	—	3	13	no	—
105	C₂×C₃²×D₄	C₂×D₃	1	13	yes	—
106	C₂²×C₃²×C₄	C₂×D₃	1	13	yes	—
107	C₂²×C₃²×C₄	C₂×D₃	1	13	yes	complemented
108	C₂×#638	—	3	13	no	—
109	C₂×#638	—	3	13	no	—
110	C₂×#638	—	3	13	no	—
111	C₂×#638	—	3	13	no	—
112	C₂²×C₃⋊Dic₃	—	3	13	no	—
113	#3828	—	6	52	no	—
114	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
115	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
116	C₂×C₄×C₃⋊D₃	—	3	13	no	—
117	C₂×C₄×C₃⋊D₃	—	3	13	no	—
118	C₂×C₄×C₃⋊D₃	—	3	13	no	—
119	C₂×C₄×C₃⋊D₃	—	3	13	no	—
120	C₂×C₄×C₃⋊D₃	—	3	13	no	—
121	C₂×C₄×C₃⋊D₃	—	6	52	no	—
122	C₂×#634	—	3	13	no	—
123	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	complemented
124	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	—
125	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	complemented
126	C₃²×C₄²	C₂×D₃	1	13	yes	complemented
127	#3757	—	3	13	no	—
128	#3757	—	3	13	no	—
129	#3752	—	3	13	no	—
130	#3752	—	3	13	no	—
131	#3752	—	3	13	no	—
132	#3752	—	3	13	no	—
133	#3752	—	3	13	no	—
134	#3752	—	3	13	no	—
135	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
136	#3750	—	3	13	no	—
137	#3750	—	3	13	no	—
138	#3750	—	3	13	no	—
139	#3750	—	3	13	no	—
140	C₄×C₃⋊Dic₃	—	3	13	no	—
141	C₂²×C₃³	—	2	1	no	—
142	C₂²×C₃³	—	2	1	no	—
143	C₂²×C₃³	—	2	1	no	—
144	C₂²×C₃³	—	2	1	no	—
145	C₂²×C₃³	—	2	1	no	—
146	C₂²×C₃³	#41	1	2	yes	complemented
147	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
148	C₂×C₃⋊(C₃⋊D₃)	—	2	8	no	—
149	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
150	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
151	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
152	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
153	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
154	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
155	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
156	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	2	yes	—
157	C₂×C₃⋊(C₃⋊D₃)	#41	1	2	yes	complemented
158	C₃³×C₄	—	2	1	no	—
159	C₃³×C₄	—	2	1	no	—
160	C₃³×C₄	—	2	1	no	—
161	C₃³×C₄	—	2	1	no	—
162	C₃³×C₄	C₂×D₄	1	2	yes	—
163	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
164	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
165	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
166	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
167	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	2	yes	—
168	C₂×#235	—	9	13	no	—
169	C₂²×C₄×D₃	—	9	13	no	—
170	C₃×C₄×D₄	C₃⋊D₃	1	13	yes	complemented
171	#939	—	9	13	no	—
172	#937	—	9	13	no	—
173	C₄×#67	—	9	13	no	—
174	C₄×#67	—	9	13	no	—
175	#896	—	9	13	no	—
176	#894	—	9	13	no	—
177	#884	—	9	13	no	—
178	#883	—	9	13	no	—
179	#882	—	9	13	no	—
180	#878	—	9	13	no	—
181	C₄×D₁₂	—	9	13	no	—
182	#872	—	9	13	no	—
183	C₂³×C₃²	C₂²×D₃	1	13	yes	—
184	C₂³×C₃²	C₂²×D₃	1	13	yes	—
185	C₂²×C₃⋊D₃	—	3	13	no	—
186	C₂²×C₃⋊D₃	—	3	13	no	—
187	C₂²×C₃⋊D₃	—	3	13	no	—
188	C₂²×C₃⋊D₃	—	6	26	no	—
189	C₂²×C₃⋊D₃	—	6	26	no	—
190	C₂²×C₃⋊D₃	—	6	26	no	—
191	C₃²×D₄	—	2	26	no	—
192	C₂×C₃²×C₄	—	2	26	no	—
193	C₂×C₃²×C₄	—	2	26	no	—
194	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
195	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
196	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
197	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
198	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
199	#638	—	6	26	no	—
200	#638	—	6	26	no	—
201	#638	—	6	26	no	—
202	#638	—	6	26	no	—
203	C₂×C₃⋊Dic₃	—	3	13	no	—
204	C₂×C₃⋊Dic₃	—	3	13	no	—
205	C₂×C₃⋊Dic₃	—	3	13	no	—
206	C₂×C₃⋊Dic₃	—	3	13	no	—
207	C₂×C₃⋊Dic₃	—	3	13	no	—
208	C₂×C₃⋊Dic₃	—	6	26	no	—
209	C₄⋊(C₃⋊D₃)	—	6	26	no	—
210	C₄⋊(C₃⋊D₃)	—	6	26	no	—
211	C₄×C₃⋊D₃	—	3	52	no	—
212	C₄×C₃⋊D₃	—	6	26	no	—
213	C₄×C₃⋊D₃	—	6	26	no	—
214	C₄×C₃⋊D₃	—	6	26	no	—
215	C₄×C₃⋊D₃	—	6	26	no	—
216	#634	—	6	26	no	—
217	#525	—	27	1	no	Sylow
218	C₂×C₃³	—	2	2	no	—
219	C₂×C₃³	—	4	1	no	—
220	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₃³	C₂×#41	1	1	yes	characteristic
222	C₂×C₃³	C₂×#41	1	1	yes	characteristic
223	C₃⋊(C₃⋊D₃)	—	2	2	no	—
224	C₃⋊(C₃⋊D₃)	—	2	2	no	—
225	C₃⋊(C₃⋊D₃)	—	4	1	no	—
226	C₂³×D₃	—	9	13	no	—
227	C₂×C₃×D₄	C₂×C₃⋊D₃	1	13	yes	—
228	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
229	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	13	yes	complemented
230	C₂×#67	—	9	13	no	—
231	C₂×#67	—	9	13	no	—
232	C₂×#67	—	9	13	no	—
233	C₂×#67	—	9	13	no	—
234	C₂²×Dic₃	—	9	13	no	—
235	#235	—	18	52	no	—
236	C₂×D₁₂	—	9	13	no	—
237	C₂×D₁₂	—	9	13	no	—
238	C₂×C₄×D₃	—	9	13	no	—
239	C₂×C₄×D₃	—	9	13	no	—
240	C₂×C₄×D₃	—	9	13	no	—
241	C₂×C₄×D₃	—	9	13	no	—
242	C₂×C₄×D₃	—	9	13	no	—
243	C₂×C₄×D₃	—	18	52	no	—
244	C₂×Dic₆	—	9	13	no	—
245	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
246	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
247	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
248	C₃×C₄²	C₂×C₃⋊D₃	1	13	yes	complemented
249	#217	—	9	13	no	—
250	#217	—	9	13	no	—
251	(C₂×D₃)⋊C₄	—	9	13	no	—
252	(C₂×D₃)⋊C₄	—	9	13	no	—
253	(C₂×D₃)⋊C₄	—	9	13	no	—
254	(C₂×D₃)⋊C₄	—	9	13	no	—
255	(C₂×D₃)⋊C₄	—	9	13	no	—
256	(C₂×D₃)⋊C₄	—	9	13	no	—
257	C₄⋊Dic₃	—	9	13	no	—
258	Dic₃⋊C₄	—	9	13	no	—
259	Dic₃⋊C₄	—	9	13	no	—
260	Dic₃⋊C₄	—	9	13	no	—
261	Dic₃⋊C₄	—	9	13	no	—
262	C₄×Dic₃	—	9	13	no	—
263	C₂²×C₃²	—	2	13	no	—
264	C₂²×C₃²	—	2	13	no	—
265	C₂²×C₃²	—	2	13	no	—
266	C₂²×C₃²	—	2	13	no	—
267	C₂²×C₃²	—	2	13	no	—
268	C₂²×C₃²	#235	1	26	yes	complemented
269	C₂²×C₃²	C₂³×D₃	1	13	yes	—
270	C₂×C₃⋊D₃	—	3	26	no	—
271	C₂×C₃⋊D₃	—	3	26	no	—
272	C₂×C₃⋊D₃	—	6	104	no	—
273	C₂×C₃⋊D₃	—	6	13	no	—
274	C₂×C₃⋊D₃	—	6	13	no	—
275	C₂×C₃⋊D₃	—	6	13	no	—
276	C₂×C₃⋊D₃	—	6	13	no	—
277	C₂×C₃⋊D₃	—	6	13	no	—
278	C₂×C₃⋊D₃	—	6	13	no	—
279	C₂×C₃⋊D₃	—	6	13	no	—
280	C₃²×C₄	—	2	13	no	—
281	C₃²×C₄	—	2	13	no	—
282	C₃²×C₄	—	2	13	no	—
283	C₃²×C₄	—	2	13	no	—
284	C₃²×C₄	D₃×D₄	1	26	yes	—
285	C₃⋊Dic₃	—	3	26	no	—
286	C₃⋊Dic₃	—	6	13	no	—
287	C₃⋊Dic₃	—	6	13	no	—
288	C₃⋊Dic₃	—	6	13	no	—
289	C₃⋊Dic₃	—	6	13	no	—
290	C₂×#41	—	27	1	no	—
291	C₂³×C₄	—	27	1	no	—
292	#123	—	27	1	no	—
293	#123	—	27	1	no	—
294	C₂²⋊Q₈	—	27	1	no	—
295	C₂²⋊Q₈	—	27	1	no	—
296	#121	—	27	1	no	—
297	#121	—	27	1	no	—
298	#120	—	27	1	no	—
299	#120	—	27	1	no	—
300	C₄×D₄	—	27	1	no	—
301	C₄×D₄	—	27	1	no	—
302	C₄×D₄	—	27	1	no	—
303	C₄×D₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
304	#117	—	27	1	no	—
305	C₃³	#525	1	1	yes	characteristic, complemented, Sylow
306	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
307	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
308	C₂²×D₃	—	9	13	no	—
309	C₂²×D₃	—	9	13	no	—
310	C₂²×D₃	—	9	13	no	—
311	C₂²×D₃	—	18	26	no	—
312	C₂²×D₃	—	18	26	no	—
313	C₂²×D₃	—	18	26	no	—
314	C₃×D₄	—	2	26	no	—
315	C₂×C₃×C₄	—	2	26	no	—
316	C₂×C₃×C₄	—	2	26	no	—
317	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
318	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
319	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
320	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
321	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
322	#67	—	18	26	no	—
323	#67	—	18	26	no	—
324	#67	—	18	26	no	—
325	#67	—	18	26	no	—
326	C₂×Dic₃	—	9	13	no	—
327	C₂×Dic₃	—	9	13	no	—
328	C₂×Dic₃	—	9	13	no	—
329	C₂×Dic₃	—	9	13	no	—
330	C₂×Dic₃	—	9	13	no	—
331	C₂×Dic₃	—	18	26	no	—
332	D₁₂	—	18	26	no	—
333	D₁₂	—	18	26	no	—
334	C₄×D₃	—	9	52	no	—
335	C₄×D₃	—	18	26	no	—
336	C₄×D₃	—	18	26	no	—
337	C₄×D₃	—	18	26	no	—
338	C₄×D₃	—	18	26	no	—
339	Dic₆	—	18	26	no	—
340	C₂×C₃²	—	2	26	no	—
341	C₂×C₃²	—	4	13	no	—
342	C₂×C₃²	C₂×#235	1	13	yes	—
343	C₂×C₃²	C₂×D₃×D₄	1	13	yes	—
344	C₂×C₃²	D₃×#41	1	13	yes	—
345	C₃⋊D₃	—	6	26	no	—
346	C₃⋊D₃	—	6	26	no	—
347	C₃⋊D₃	—	12	13	no	—
348	C₂⁴	—	27	1	no	—
349	#41	—	54	4	no	—
350	C₂×Q₈	—	27	1	no	—
351	C₂×D₄	—	27	1	no	—
352	C₂×D₄	—	27	1	no	—
353	C₂×D₄	—	27	1	no	—
354	C₂×D₄	—	27	1	no	—
355	C₂×D₄	—	27	1	no	—
356	C₂×D₄	—	27	1	no	—
357	C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
358	C₂²×C₄	—	27	1	no	—
359	C₂²×C₄	—	27	1	no	—
360	C₂²×C₄	—	27	1	no	—
361	C₂²×C₄	—	27	1	no	—
362	C₂²×C₄	—	27	1	no	—
363	C₂²×C₄	—	27	1	no	—
364	C₂²×C₄	—	54	4	no	—
365	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
367	C₄⋊C₄	—	27	1	no	—
368	C₄⋊C₄	—	27	1	no	—
369	C₄⋊C₄	—	27	1	no	—
370	C₄⋊C₄	—	27	1	no	—
371	C₄⋊C₄	—	27	1	no	—
372	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
373	C₂²⋊C₄	—	27	1	no	—
374	C₂²⋊C₄	—	27	1	no	—
375	C₂²⋊C₄	—	27	1	no	—
376	C₂²⋊C₄	—	27	1	no	—
377	C₂²⋊C₄	—	27	1	no	—
378	C₂²⋊C₄	—	27	1	no	—
379	C₂²⋊C₄	—	27	1	no	—
380	C₂²⋊C₄	—	27	1	no	—
381	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
382	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
383	C₄²	—	27	1	no	—
384	C₄²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
385	C₂²×C₃	—	2	13	no	—
386	C₂²×C₃	—	2	13	no	—
387	C₂²×C₃	—	2	13	no	—
388	C₂²×C₃	—	2	13	no	—
389	C₂²×C₃	—	2	13	no	—
390	C₂²×C₃	#3828	1	26	yes	complemented
391	C₂²×C₃	C₂³×C₃⋊D₃	1	13	yes	—
392	C₂×D₃	—	9	26	no	—
393	C₂×D₃	—	9	26	no	—
394	C₂×D₃	—	18	104	no	—
395	C₂×D₃	—	18	13	no	—
396	C₂×D₃	—	18	13	no	—
397	C₂×D₃	—	18	13	no	—
398	C₂×D₃	—	18	13	no	—
399	C₂×D₃	—	18	13	no	—
400	C₂×D₃	—	18	13	no	—
401	C₂×D₃	—	18	13	no	—
402	C₃×C₄	—	2	13	no	—
403	C₃×C₄	—	2	13	no	—
404	C₃×C₄	—	2	13	no	—
405	C₃×C₄	—	2	13	no	—
406	C₃×C₄	D₄×C₃⋊D₃	1	26	yes	—
407	Dic₃	—	9	26	no	—
408	Dic₃	—	18	13	no	—
409	Dic₃	—	18	13	no	—
410	Dic₃	—	18	13	no	—
411	Dic₃	—	18	13	no	—
412	C₃²	#5547	1	13	yes	complemented
413	C₂³	—	27	1	no	—
414	C₂³	—	27	1	no	—
415	C₂³	—	27	1	no	—
416	C₂³	—	54	2	no	—
417	C₂³	—	54	2	no	—
418	C₂³	—	54	2	no	—
419	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
420	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
421	Q₈	—	54	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	54	2	no	—
424	D₄	—	54	2	no	—
425	D₄	—	54	2	no	—
426	D₄	—	54	2	no	—
427	D₄	—	54	2	no	—
428	D₄	—	54	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	27	1	no	—
432	C₂×C₄	—	27	4	no	—
433	C₂×C₄	—	27	1	no	—
434	C₂×C₄	—	27	1	no	—
435	C₂×C₄	—	27	1	no	—
436	C₂×C₄	—	27	1	no	—
437	C₂×C₄	—	54	2	no	—
438	C₂×C₄	—	54	2	no	—
439	C₂×C₄	—	54	2	no	—
440	C₂×C₄	—	54	2	no	—
441	C₂×C₄	—	54	2	no	—
442	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
445	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
447	C₂×C₃	—	2	26	no	—
448	C₂×C₃	—	4	13	no	—
449	C₂×C₃	C₂×#3828	1	13	yes	—
450	C₂×C₃	C₂×D₄×C₃⋊D₃	1	13	yes	—
451	C₂×C₃	#41×C₃⋊D₃	1	13	yes	—
452	D₃	—	18	26	no	—
453	D₃	—	18	26	no	—
454	D₃	—	36	13	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	27	2	no	—
461	C₂²	—	27	2	no	—
462	C₂²	—	54	8	no	—
463	C₂²	—	54	1	no	—
464	C₂²	—	54	1	no	—
465	C₂²	—	54	1	no	—
466	C₂²	—	54	1	no	—
467	C₂²	—	54	1	no	—
468	C₂²	—	54	1	no	—
469	C₂²	—	54	1	no	—
470	C₂²	#89076	1	2	yes	complemented
471	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	27	2	no	—
477	C₄	—	54	1	no	—
478	C₄	—	54	1	no	—
479	C₄	—	54	1	no	—
480	C₄	—	54	1	no	—
481	C₄	D₄×C₃⋊(C₃⋊D₃)	1	2	yes	—
482	C₃	#10596018	1	13	yes	complemented
483	C₂	—	2	2	no	—
484	C₂	—	4	1	no	—
485	C₂	—	54	2	no	—
486	C₂	—	54	2	no	—
487	C₂	—	108	1	no	—
488	C₂	C₂×#89076	1	1	yes	characteristic
489	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
490	C₂	#41×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)
commutator, socle, cosocle	C₂²×C₃³	C₂⁴
Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
Fitting	C₃³×C₄×D₄	C₂
hypercenter	C₄×D₄	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#525
LCS	G ▷ C₂²×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#89076	C₂	semidirect
2. C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
3. C₃³×C₄×D₄	C₂	semidirect
4. #11723980	C₂	semidirect
5. #11723978	C₂	semidirect
6. C₄×#6312	C₂	semidirect
7. C₄×#6312	C₂	semidirect
8. #11723937	C₂	semidirect
9. #11723935	C₂	semidirect
10. #11723925	C₂	semidirect
11. #11723924	C₂	semidirect
12. #11723923	C₂	semidirect
13. #11723919	C₂	semidirect
14. C₄×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	semidirect
15. #11723913	C₂	semidirect
20. C₂²×C₃³×C₄	C₂²	semidirect
24. C₂×#6312	C₂²	semidirect
34. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
35. C₂×#6308	C₂²	semidirect
36. C₃³×C₄⋊C₄	C₂²	semidirect
38. C₃³×C₂²⋊C₄	C₂²	semidirect
39. C₃³×C₄²	C₂²	semidirect
41. #88864	C₂²	semidirect
46. #88859	C₂²	semidirect
47. #88859	C₂²	semidirect
48. C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	semidirect
49. #88857	C₂²	semidirect
50. #88857	C₂²	semidirect
51. #88857	C₂²	semidirect
52. #88857	C₂²	semidirect
53. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
56. C₃²×C₄×D₄	D₃	semidirect
101. C₄×C₃⋊(C₃⋊D₃)	D₄	semidirect
107. C₂²×C₃²×C₄	C₂×D₃	semidirect
123. C₃²×C₄⋊C₄	C₂×D₃	semidirect
125. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
126. C₃²×C₄²	C₂×D₃	semidirect
146. C₂²×C₃³	#41	semidirect
157. C₂×C₃⋊(C₃⋊D₃)	#41	semidirect
170. C₃×C₄×D₄	C₃⋊D₃	semidirect
229. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
245. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
247. C₃×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
248. C₃×C₄²	C₂×C₃⋊D₃	semidirect
268. C₂²×C₃²	#235	semidirect
303. C₄×D₄	C₃⋊(C₃⋊D₃)	semidirect
305. C₃³	#525	semidirect
366. C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
372. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
382. C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
384. C₄²	C₂×C₃⋊(C₃⋊D₃)	semidirect
390. C₂²×C₃	#3828	semidirect
412. C₃²	#5547	semidirect
470. C₂²	#89076	semidirect
482. C₃	#10596018	semidirect

Maximal subgroups

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

subgroup	index
C₂×#89076	2
C₂²×C₄×C₃⋊(C₃⋊D₃)	2
C₃³×C₄×D₄	2
#11723980	2
#11723978	2
C₄×#6312	2
#11723937	2
#11723935	2
#11723925	2
#11723924	2
#11723923	2
#11723919	2
C₄×C₄⋊(C₃⋊(C₃⋊D₃))	2
#11723913	2
#10596018	3