Subgroups — #11785214

Order 1152.

709 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×Dic₆	C₂	1	1	yes	maximal, characteristic
2	#10592634	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₂×#63566	C₂	1	2	yes	maximal
5	#10589164	C₂	1	2	yes	maximal
6	#71626	—	3	1	no	maximal
7	#70485	—	3	1	no	maximal
8	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
9	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
11	C₂×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
12	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×Dic₃⋊C₄	—	2	1	no	—
15	C₂×C₃×C₄×Dic₃	—	2	1	no	—
16	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
17	C₃×C₄×Dic₆	—	2	2	no	—
18	C₃×C₄×Dic₆	C₄	1	4	yes	complemented
19	C₃×C₄⋊(C₃⋊C₈)	—	2	2	no	—
20	#63566	—	2	4	no	—
21	C₂×C₃×C₄×Q₈	—	3	1	no	—
22	C₂×C₄×Dic₆	D₃	1	1	yes	characteristic
23	C₂×C₃×C₄⋊C₈	—	3	1	no	—
24	C₂×#835	—	3	2	no	—
25	C₂×#816	—	3	2	no	—
26	#4935	—	3	1	no	—
27	#4935	—	3	1	no	—
28	#4935	—	6	1	no	—
29	C₂×C₄⋊(C₃⋊C₈)	D₃	1	1	yes	characteristic
30	#4551	—	3	2	no	—
31	#4529	—	3	2	no	—
32	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
33	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
34	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
35	C₂²×C₃⋊Dic₃	—	2	2	no	—
36	C₂²×C₃×Dic₃	—	2	1	no	—
37	C₂²×C₃×Dic₃	—	2	1	no	—
38	C₂×C₃×Dic₆	—	2	1	no	—
39	C₂×C₃×Dic₆	—	2	1	no	—
40	C₂×C₃×Dic₆	—	2	1	no	—
41	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
42	C₂×C₃×Dic₆	D₄	1	2	yes	—
43	C₂×C₃×Dic₆	Q₈	1	2	yes	—
44	C₃²×C₄²	C₂×C₄	1	2	yes	—
45	C₃²×C₄²	D₄	1	2	yes	—
46	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
47	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
48	C₄⋊(C₃⋊Dic₃)	—	4	2	no	—
49	C₄⋊(C₃⋊Dic₃)	—	4	2	no	—
50	C₃×C₄⋊Dic₃	—	2	1	no	—
51	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
52	C₃×Dic₃⋊C₄	—	2	4	no	—
53	C₃×C₄×Dic₃	—	2	4	no	—
54	C₂×C₃×C₃⋊C₈	—	2	2	no	—
55	C₂×C₃×C₃⋊C₈	—	2	2	no	—
56	C₂×C₃×C₃⋊C₈	—	2	2	no	—
57	#1803	—	9	1	no	Sylow
58	C₂²×C₃×Q₈	—	3	1	no	—
59	C₂²×Dic₆	C₂×D₃	1	1	yes	characteristic
60	C₂²×C₃×C₈	—	3	2	no	—
61	C₃×C₄×Q₈	—	3	4	no	—
62	C₃×C₄×Q₈	—	6	2	no	—
63	C₂×C₃×C₄⋊C₄	—	3	1	no	—
64	C₂×C₃×C₄⋊C₄	—	6	1	no	—
65	C₂×C₃×C₄²	—	2	1	no	—
66	C₂×C₃×C₄²	—	6	1	no	—
67	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
68	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
69	C₂×C₄⋊Dic₃	—	3	2	no	—
70	C₂×C₄⋊Dic₃	—	3	2	no	—
71	C₂×C₄⋊Dic₃	—	6	2	no	—
72	C₂×C₄⋊Dic₃	—	6	2	no	—
73	C₂×C₄⋊Dic₃	—	6	2	no	—
74	C₂×C₄⋊Dic₃	—	6	1	no	—
75	C₂×C₄⋊Dic₃	—	6	1	no	—
76	C₂×C₄⋊Dic₃	—	6	1	no	—
77	C₂×C₄⋊Dic₃	—	6	1	no	—
78	C₂×C₄⋊Dic₃	C₂×D₃	1	1	yes	characteristic
79	C₂×Dic₃⋊C₄	—	2	1	no	—
80	C₂×C₄×Dic₃	—	2	1	no	—
81	C₂²×C₃⋊C₈	C₂×D₃	1	2	yes	—
82	C₄×Dic₆	—	2	2	no	—
83	C₄×Dic₆	Dic₃	1	4	yes	complemented
84	C₃×C₄⋊C₈	—	6	2	no	—
85	#835	—	6	4	no	—
86	#816	—	6	4	no	—
87	C₄⋊(C₃⋊C₈)	—	2	2	no	—
88	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃²×C₄	—	2	1	no	—
90	C₂×C₃²×C₄	—	2	1	no	—
91	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
92	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
93	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
94	C₂×C₃²×C₄	Q₁₆	1	2	yes	—
95	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
99	C₂×C₃²×C₄	#41	1	1	yes	characteristic
100	C₂×C₃²×C₄	#41	1	1	yes	characteristic
101	C₂×C₃⋊Dic₃	—	4	2	no	—
102	C₂×C₃⋊Dic₃	—	4	2	no	—
103	C₂×C₃⋊Dic₃	—	4	2	no	—
104	C₂×C₃×Dic₃	—	2	2	no	—
105	C₂×C₃×Dic₃	—	2	2	no	—
106	C₂×C₃×Dic₃	—	2	2	no	—
107	C₂×C₃×Dic₃	—	2	2	no	—
108	C₂×C₃×Dic₃	—	4	1	no	—
109	C₂×C₃×Dic₃	—	4	1	no	—
110	C₃×Dic₆	—	2	2	no	—
111	C₃×Dic₆	—	2	2	no	—
112	C₃×Dic₆	—	2	2	no	—
113	C₃×Dic₆	C₄⋊C₄	1	4	yes	complemented
114	C₃×C₃⋊C₈	—	4	2	no	—
115	C₂×C₄×Q₈	—	3	1	no	—
116	C₂×C₄⋊C₈	—	3	1	no	—
117	C₂×#103	—	9	2	no	—
118	#384	—	9	1	no	—
119	#340	—	9	2	no	—
120	C₂×C₃×Q₈	—	3	2	no	—
121	C₂×C₃×Q₈	—	3	2	no	—
122	C₂×C₃×Q₈	—	3	2	no	—
123	C₂×C₃×Q₈	—	6	1	no	—
124	C₂×C₃×Q₈	—	6	1	no	—
125	C₂×C₃×Q₈	—	6	1	no	—
126	C₂²×C₃×C₄	—	2	1	no	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	2	1	no	—
129	C₂²×C₃×C₄	—	6	1	no	—
130	C₂²×C₃×C₄	—	6	1	no	—
131	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
132	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
133	C₂²×C₃×C₄	#67	1	1	yes	characteristic
134	C₂²×C₃×C₄	#67	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
137	C₂²×Dic₃	—	2	1	no	—
138	C₂²×Dic₃	—	2	1	no	—
139	C₂²×Dic₃	—	6	4	no	—
140	C₂²×Dic₃	—	6	2	no	—
141	C₂²×Dic₃	—	6	2	no	—
142	C₂×Dic₆	—	2	1	no	—
143	C₂×Dic₆	—	2	1	no	—
144	C₂×Dic₆	—	2	1	no	—
145	C₂×Dic₆	Dic₆	1	2	yes	—
146	C₂×Dic₆	D₁₂	1	2	yes	—
147	C₂×Dic₆	C₂×Dic₃	1	2	yes	—
148	C₂×C₃×C₈	—	6	2	no	—
149	C₂×C₃×C₈	—	6	2	no	—
150	C₂×C₃×C₈	—	6	2	no	—
151	C₃×C₄⋊C₄	—	3	2	no	—
152	C₃×C₄⋊C₄	—	6	4	no	—
153	C₃×C₄⋊C₄	—	6	1	no	—
154	C₃×C₄²	—	2	2	no	—
155	C₃×C₄²	—	2	2	no	—
156	C₃×C₄²	—	6	4	no	—
157	C₃×C₄²	C₄×D₃	1	2	yes	—
158	C₃×C₄²	C₂×Dic₃	1	2	yes	—
159	C₃×C₄²	#67	1	2	yes	—
160	C₃×C₄²	#67	1	2	yes	—
161	C₄⋊Dic₃	—	2	1	no	—
162	C₄⋊Dic₃	—	6	2	no	—
163	C₄⋊Dic₃	—	6	2	no	—
164	C₄⋊Dic₃	—	6	2	no	—
165	C₄⋊Dic₃	—	6	2	no	—
166	C₄⋊Dic₃	—	12	2	no	—
167	C₄⋊Dic₃	—	12	2	no	—
168	C₄⋊Dic₃	—	12	4	no	—
169	C₄⋊Dic₃	—	12	2	no	—
170	C₄⋊Dic₃	—	12	2	no	—
171	C₄⋊Dic₃	—	12	4	no	—
172	C₄⋊Dic₃	—	12	2	no	—
173	C₄⋊Dic₃	—	12	2	no	—
174	C₄⋊Dic₃	C₂×Dic₃	1	2	yes	—
175	Dic₃⋊C₄	—	2	4	no	—
176	C₄×Dic₃	—	2	4	no	—
177	C₂×C₃⋊C₈	—	2	2	no	—
178	C₂×C₃⋊C₈	—	2	2	no	—
179	C₂×C₃⋊C₈	—	2	2	no	—
180	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₃²	#121	1	1	yes	characteristic
182	C₂²×C₃²	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
184	C₂²×C₃²	C₂×Q₁₆	1	1	yes	characteristic
185	C₂²×C₃²	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂²×C₃²	#137	1	1	yes	characteristic
187	C₃²×C₄	—	2	2	no	—
188	C₃²×C₄	#103	1	4	yes	complemented
189	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₃²×C₄	#117	1	1	yes	characteristic
191	C₃²×C₄	#121	1	1	yes	characteristic
192	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
193	C₃⋊Dic₃	—	8	2	no	—
194	C₃×Dic₃	—	2	4	no	—
195	C₃×Dic₃	—	4	2	no	—
196	C₂²×Q₈	—	3	1	no	—
197	C₂²×C₈	—	3	2	no	—
198	C₄×Q₈	—	3	4	no	—
199	C₄×Q₈	—	6	2	no	—
200	C₂×C₄⋊C₄	—	3	1	no	—
201	C₂×C₄⋊C₄	—	6	1	no	—
202	C₂×C₄⋊C₄	—	9	2	no	—
203	C₂×C₄⋊C₄	—	18	1	no	—
204	C₂×C₄⋊C₄	—	18	1	no	—
205	C₂×C₄²	—	6	1	no	—
206	C₂×C₄²	D₃²	1	1	yes	characteristic
207	C₄⋊C₈	—	6	2	no	—
208	#103	—	18	4	no	—
209	C₂³×C₃	—	2	1	no	—
210	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
211	C₂³×C₃	C₂×#67	1	1	yes	characteristic
212	C₃×Q₈	—	3	4	no	—
213	C₃×Q₈	—	6	2	no	—
214	C₃×Q₈	—	6	2	no	—
215	C₃×Q₈	—	6	2	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	6	2	no	—
233	C₂×C₃×C₄	—	6	2	no	—
234	C₂×C₃×C₄	—	6	2	no	—
235	C₂×C₃×C₄	—	6	2	no	—
236	C₂×C₃×C₄	—	12	1	no	—
237	C₂×C₃×C₄	—	12	1	no	—
238	C₂×C₃×C₄	#204	1	2	yes	—
239	C₂×C₃×C₄	Dic₁₂	1	2	yes	—
240	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
241	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
242	C₂×C₃×C₄	#215	1	2	yes	—
243	C₂×C₃×C₄	#216	1	2	yes	—
244	C₂×C₃×C₄	#217	1	2	yes	—
245	C₂×C₃×C₄	#217	1	2	yes	—
246	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
249	C₂×C₃×C₄	#235	1	1	yes	characteristic
250	C₂×C₃×C₄	#235	1	1	yes	characteristic
251	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	#237	1	1	yes	characteristic
253	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
254	C₂×C₃×C₄	#239	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
258	C₂×Dic₃	—	2	2	no	—
259	C₂×Dic₃	—	2	2	no	—
260	C₂×Dic₃	—	2	2	no	—
261	C₂×Dic₃	—	2	2	no	—
262	C₂×Dic₃	—	4	1	no	—
263	C₂×Dic₃	—	4	1	no	—
264	C₂×Dic₃	—	12	4	no	—
265	C₂×Dic₃	—	12	4	no	—
266	C₂×Dic₃	—	12	4	no	—
267	C₂×Dic₃	—	12	2	no	—
268	C₂×Dic₃	—	12	2	no	—
269	C₂×Dic₃	—	12	2	no	—
270	C₂×Dic₃	—	12	2	no	—
271	C₂×Dic₃	—	12	2	no	—
272	C₂×Dic₃	—	12	2	no	—
273	Dic₆	—	2	2	no	—
274	Dic₆	—	2	2	no	—
275	Dic₆	—	2	2	no	—
276	Dic₆	C₄⋊Dic₃	1	4	yes	complemented
277	C₃×C₈	—	12	2	no	—
278	C₃⋊C₈	—	4	2	no	—
279	C₂×C₃²	#380	1	1	yes	characteristic
280	C₂×C₃²	C₂×#103	1	1	yes	characteristic
281	C₂×C₃²	#417	1	1	yes	characteristic
282	C₂×C₃²	#460	1	1	yes	characteristic
283	C₂×C₃²	#462	1	1	yes	characteristic
284	C₂×C₃²	#475	1	1	yes	characteristic
285	C₂×C₃²	#477	1	1	yes	characteristic
286	C₂×Q₈	—	3	2	no	—
287	C₂×Q₈	—	3	2	no	—
288	C₂×Q₈	—	3	2	no	—
289	C₂×Q₈	—	6	1	no	—
290	C₂×Q₈	—	6	1	no	—
291	C₂×Q₈	—	6	1	no	—
292	C₂²×C₄	—	6	1	no	—
293	C₂²×C₄	—	6	1	no	—
294	C₂²×C₄	—	18	2	no	—
295	C₂²×C₄	#626	1	1	yes	characteristic
296	C₂²×C₄	#626	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
298	C₂×C₈	—	6	2	no	—
299	C₂×C₈	—	6	2	no	—
300	C₂×C₈	—	6	2	no	—
301	C₄⋊C₄	—	3	2	no	—
302	C₄⋊C₄	—	6	4	no	—
303	C₄⋊C₄	—	6	1	no	—
304	C₄⋊C₄	—	18	2	no	—
305	C₄⋊C₄	—	18	2	no	—
306	C₄⋊C₄	—	36	2	no	—
307	C₄⋊C₄	—	36	2	no	—
308	C₄²	—	6	4	no	—
309	C₄²	D₃×Dic₃	1	2	yes	—
310	C₄²	#625	1	2	yes	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	2	1	no	—
313	C₂²×C₃	—	2	1	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	#895	1	1	yes	characteristic
319	C₂²×C₃	#897	1	1	yes	characteristic
320	C₂²×C₃	C₂×#204	1	1	yes	characteristic
321	C₂²×C₃	C₂×Dic₁₂	1	1	yes	characteristic
322	C₂²×C₃	#908	1	1	yes	characteristic
323	C₂²×C₃	#909	1	1	yes	characteristic
324	C₂²×C₃	#924	1	1	yes	characteristic
325	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
326	C₂²×C₃	#930	1	1	yes	characteristic
327	C₂²×C₃	C₂×#215	1	1	yes	characteristic
328	C₂²×C₃	C₂×#216	1	1	yes	characteristic
329	C₂²×C₃	#949	1	1	yes	characteristic
330	C₂²×C₃	#951	1	1	yes	characteristic
331	C₂²×C₃	C₂×#217	1	1	yes	characteristic
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	6	4	no	—
341	C₃×C₄	—	12	2	no	—
342	C₃×C₄	#816	1	4	yes	complemented
343	C₃×C₄	#835	1	4	yes	complemented
344	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
345	C₃×C₄	#892	1	1	yes	characteristic
346	C₃×C₄	#924	1	1	yes	characteristic
347	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
348	C₃×C₄	#926	1	1	yes	characteristic
349	C₃×C₄	#930	1	1	yes	characteristic
350	C₃×C₄	#938	1	1	yes	characteristic
351	C₃×C₄	#946	1	1	yes	characteristic
352	Dic₃	—	2	4	no	—
353	Dic₃	—	4	2	no	—
354	Dic₃	—	24	4	no	—
355	Dic₃	—	24	2	no	—
356	Dic₃	—	24	2	no	—
357	C₃²	#1803	1	1	yes	characteristic, complemented, Sylow
358	C₂³	C₂×#626	1	1	yes	characteristic
359	Q₈	—	3	4	no	—
360	Q₈	—	6	2	no	—
361	Q₈	—	6	2	no	—
362	Q₈	—	6	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	—	6	2	no	—
367	C₂×C₄	—	6	2	no	—
368	C₂×C₄	—	6	2	no	—
369	C₂×C₄	—	12	1	no	—
370	C₂×C₄	—	12	1	no	—
371	C₂×C₄	—	36	2	no	—
372	C₂×C₄	—	36	2	no	—
373	C₂×C₄	—	36	2	no	—
374	C₂×C₄	#3717	1	2	yes	—
375	C₂×C₄	#3719	1	2	yes	—
376	C₂×C₄	(C₂×D₃)⋊Dic₃	1	2	yes	—
377	C₂×C₄	(C₂×D₃)⋊Dic₃	1	2	yes	—
378	C₂×C₄	D₃×Dic₆	1	1	yes	characteristic
379	C₂×C₄	#3795	1	1	yes	characteristic
380	C₂×C₄	#3799	1	1	yes	characteristic
381	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
382	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
383	C₂×C₄	C₂×#625	1	1	yes	characteristic
384	C₈	—	12	2	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	2	1	no	—
390	C₂×C₃	—	2	1	no	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	#4848	1	1	yes	characteristic
393	C₂×C₃	#4849	1	1	yes	characteristic
394	C₂×C₃	#4850	1	1	yes	characteristic
395	C₂×C₃	#4851	1	1	yes	characteristic
396	C₂×C₃	#4987	1	1	yes	characteristic
397	C₂×C₃	#5020	1	1	yes	characteristic
398	C₂×C₃	#5021	1	1	yes	characteristic
399	C₂×C₃	#5027	1	1	yes	characteristic
400	C₂×C₃	#5031	1	1	yes	characteristic
401	C₂×C₃	C₂×#816	1	1	yes	characteristic
402	C₂×C₃	#5133	1	1	yes	characteristic
403	C₂×C₃	#5212	1	1	yes	characteristic
404	C₂×C₃	C₂×#835	1	1	yes	characteristic
405	C₂×C₃	#5232	1	1	yes	characteristic
406	C₂²	#63825	1	1	yes	characteristic
407	C₂²	#63831	1	1	yes	characteristic
408	C₂²	C₂×#3717	1	1	yes	characteristic
409	C₂²	C₂×#3719	1	1	yes	characteristic
410	C₂²	#63857	1	1	yes	characteristic
411	C₂²	#63909	1	1	yes	characteristic
412	C₂²	C₂×(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	6	4	no	—
415	C₄	—	12	2	no	—
416	C₄	—	72	2	no	—
417	C₄	#63566	1	4	yes	complemented
418	C₄	#63841	1	1	yes	characteristic
419	C₄	#63856	1	1	yes	characteristic
420	C₄	D₃×C₄⋊Dic₃	1	1	yes	characteristic
421	C₄	#63908	1	1	yes	characteristic
422	C₃	—	2	1	no	—
423	C₃	#70485	1	1	yes	characteristic, complemented
424	C₃	#71626	1	1	yes	characteristic, complemented
425	C₂	#10590283	1	1	yes	characteristic
426	C₂	#10590301	1	1	yes	characteristic
427	C₂	#10590367	1	1	yes	characteristic
428	C₂	#10590385	1	1	yes	characteristic
429	C₂	#10591088	1	1	yes	characteristic
430	C₂	C₂×#63566	1	1	yes	characteristic
431	C₂	#10591313	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#626
commutator	C₂×C₃²×C₄	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle, prime radical	C₂³×C₃²	C₂×D₄
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	C₂×C₄²	D₃²
hypocenter	C₃²	#1803
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
18. C₃×C₄×Dic₆	C₄	semidirect
83. C₄×Dic₆	Dic₃	semidirect
113. C₃×Dic₆	C₄⋊C₄	semidirect
188. C₃²×C₄	#103	semidirect
276. Dic₆	C₄⋊Dic₃	semidirect
342. C₃×C₄	#816	semidirect
343. C₃×C₄	#835	semidirect
357. C₃²	#1803	semidirect
417. C₄	#63566	semidirect
423. C₃	#70485	semidirect
424. C₃	#71626	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×Dic₆	2
#10592634	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×#63566	2
#10589164	2
#71626	3
#70485	3