Subgroups — C₃×#79975 #11897525

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5579	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×Q₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#446	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4847	C₂	1	2	yes	maximal, complemented
5	C₃×#4846	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4842	C₂	1	2	yes	maximal, complemented
7	C₃×#4842	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4711	C₂	1	2	yes	maximal
9	C₃×#4702	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₂₄	C₂	1	1	yes	maximal, characteristic
11	C₃×#4680	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3384	—	3	1	no	maximal
13	#79975	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₃×Q₈	—	2	1	no	—
15	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
16	C₃×#946	—	2	1	no	—
17	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
18	C₃×#897	—	2	1	no	—
19	C₃×#897	—	2	2	no	—
20	C₃×#896	—	2	2	no	—
21	C₃×D₃×C₄⋊C₄	—	2	1	no	—
22	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
23	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
24	C₃×C₄×D₁₂	C₂²	1	2	yes	—
25	C₃×C₄×D₁₂	C₂²	1	2	yes	—
26	C₃×#870	C₂²	1	2	yes	—
27	C₃×#869	C₂²	1	1	yes	characteristic
28	C₃×#869	C₂²	1	1	yes	characteristic
29	C₃×#869	C₂²	1	2	yes	—
30	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
32	C₃²×#97	C₂²	1	2	yes	—
33	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
34	C₃×#821	C₂²	1	1	yes	characteristic
35	C₃×#821	C₂²	1	1	yes	characteristic
36	C₃×#821	C₂²	1	2	yes	—
37	C₃×#821	C₂²	1	2	yes	—
38	C₃×#818	C₂²	1	1	yes	characteristic
39	C₃×#818	C₂²	1	2	yes	—
40	C₃×#817	C₂²	1	2	yes	—
41	C₃×#817	C₂²	1	2	yes	—
42	C₃×#817	C₂²	1	2	yes	—
43	C₃×#554	—	3	1	no	—
44	C₃×D₄×Q₈	—	3	1	no	—
45	#5579	C₂×C₃	1	1	yes	characteristic, complemented
46	Q₈×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×#501	—	3	2	no	—
48	C₃×#498	—	3	1	no	—
49	C₃×#478	—	3	2	no	—
50	C₃×#476	—	3	2	no	—
51	C₃×#476	—	3	1	no	—
52	C₃×#474	—	3	1	no	—
53	C₃×#446	—	2	1	no	—
54	C₃×#446	D₃	1	1	yes	characteristic, complemented
55	C₃×#446	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×#442	—	3	2	no	—
57	C₃×C₄×D₈	—	3	1	no	—
58	#4847	C₂×C₃	1	2	yes	complemented
59	#4846	C₂×C₃	1	1	yes	characteristic, complemented
60	#4842	C₂×C₃	1	2	yes	complemented
61	#4842	C₂×C₃	1	1	yes	characteristic, complemented
62	#4711	C₂×C₃	1	2	yes	—
63	#4702	C₂×C₃	1	2	yes	complemented
64	C₄×D₂₄	C₂×C₃	1	1	yes	characteristic
65	#4680	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
67	C₃×D₃×Q₈	—	4	4	no	—
68	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
69	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×D₃	—	2	1	no	—
71	C₂×C₃×C₄×D₃	—	2	2	no	—
72	C₂×C₃×C₄×D₃	—	2	1	no	—
73	C₂×C₃×C₄×D₃	—	2	2	no	—
74	C₂×C₃×Dic₆	—	2	2	no	—
75	C₂×C₃×Dic₆	—	2	1	no	—
76	C₂×C₃×Dic₆	—	2	1	no	—
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₈	C₂³	1	2	yes	—
79	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
80	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₃²×C₄⋊C₄	D₄	1	2	yes	—
82	C₃²×C₄²	C₂³	1	1	yes	characteristic
83	C₃²×C₄²	C₂³	1	2	yes	—
84	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
85	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
86	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
87	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
88	C₃×C₄⋊Dic₃	—	2	1	no	—
89	C₃×C₄⋊Dic₃	—	2	2	no	—
90	C₃×C₄⋊Dic₃	—	2	1	no	—
91	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
92	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
93	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
94	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
95	C₃×Dic₃⋊C₄	—	2	2	no	—
96	C₃×Dic₃⋊C₄	—	2	2	no	—
97	C₃×D₂₄	Q₈	1	4	yes	complemented
98	#3384	—	3	1	no	Sylow
99	C₂²×C₃×Q₈	—	6	1	no	—
100	C₂×D₃×Q₈	—	2	1	no	—
101	C₂×C₃×D₈	—	3	1	no	—
102	C₃×C₄⋊Q₈	—	3	1	no	—
103	C₃×C₄⋊Q₈	—	3	2	no	—
104	C₃×C₄⋊Q₈	—	3	1	no	—
105	C₃×#125	—	3	2	no	—
106	C₃×C₂²⋊Q₈	—	6	1	no	—
107	C₃×C₂²⋊Q₈	—	6	2	no	—
108	C₃×C₂²⋊Q₈	—	6	1	no	—
109	C₃×C₂²⋊Q₈	—	6	2	no	—
110	C₃×C₄×Q₈	—	2	1	no	—
111	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
112	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₃×C₄×D₄	—	3	1	no	—
114	C₃×C₄×D₄	—	3	1	no	—
115	C₃×C₄×D₄	—	3	2	no	—
116	C₃×C₄×D₄	—	3	2	no	—
117	C₂×C₃×C₄⋊C₄	—	6	1	no	—
118	#946	—	2	1	no	—
119	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
120	#897	—	2	1	no	—
121	#897	—	2	2	no	—
122	#896	—	2	2	no	—
123	D₃×C₄⋊C₄	—	2	1	no	—
124	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
125	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
126	C₄×D₁₂	C₂²×C₃	1	2	yes	—
127	C₄×D₁₂	C₂²×C₃	1	2	yes	—
128	#870	C₂²×C₃	1	2	yes	—
129	#869	C₂²×C₃	1	1	yes	characteristic
130	#869	C₂²×C₃	1	1	yes	characteristic
131	#869	C₂²×C₃	1	2	yes	—
132	C₃×#107	—	3	1	no	—
133	C₃×#107	—	3	2	no	—
134	C₃×#106	—	3	2	no	—
135	C₃×#106	—	3	2	no	—
136	C₃×#106	—	3	2	no	—
137	C₃×C₄⋊C₈	—	2	1	no	—
138	C₃×C₄⋊C₈	—	2	2	no	—
139	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
140	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
141	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
142	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
143	C₃×#102	—	3	1	no	—
144	C₃×#102	—	3	1	no	—
145	C₃×#102	—	3	2	no	—
146	C₃×#102	—	3	2	no	—
147	C₃×#97	—	2	2	no	—
148	C₃×#97	C₂×D₃	1	2	yes	—
149	C₃×#97	C₂²×C₃	1	2	yes	—
150	C₃×C₄×C₈	—	2	1	no	—
151	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
152	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
153	#821	C₂²×C₃	1	1	yes	characteristic
154	#821	C₂²×C₃	1	1	yes	characteristic
155	#821	C₂²×C₃	1	2	yes	—
156	#821	C₂²×C₃	1	2	yes	—
157	#818	C₂²×C₃	1	1	yes	characteristic
158	#818	C₂²×C₃	1	2	yes	—
159	#817	C₂²×C₃	1	2	yes	—
160	#817	C₂²×C₃	1	2	yes	—
161	#817	C₂²×C₃	1	2	yes	—
162	C₂²×C₃×D₃	—	2	1	no	—
163	C₂²×C₃×D₃	—	2	1	no	—
164	C₃²×Q₈	—	2	2	no	—
165	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
166	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
167	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
170	C₂×C₃×Dic₃	—	2	1	no	—
171	C₂×C₃×Dic₃	—	2	2	no	—
172	C₂×C₃×Dic₃	—	2	1	no	—
173	C₂×C₃×Dic₃	—	2	2	no	—
174	C₃×D₁₂	—	2	1	no	—
175	C₃×D₁₂	—	2	1	no	—
176	C₃×D₁₂	C₂×Q₈	1	2	yes	—
177	C₃×D₁₂	C₂×Q₈	1	2	yes	complemented
178	C₃×C₄×D₃	—	4	4	no	—
179	C₃×C₄×D₃	—	4	2	no	—
180	C₃×C₄×D₃	—	4	2	no	—
181	C₃×C₄×D₃	—	8	2	no	—
182	C₃×Dic₆	—	4	4	no	—
183	C₃×Dic₆	—	4	2	no	—
184	C₃×Dic₆	—	8	1	no	—
185	C₃²×C₈	—	2	1	no	—
186	C₃²×C₈	—	2	2	no	—
187	C₃²×C₈	C₂×Q₈	1	2	yes	complemented
188	#554	—	3	1	no	—
189	D₄×Q₈	—	3	1	no	—
190	#501	—	3	2	no	—
191	#498	—	3	1	no	—
192	#478	—	3	2	no	—
193	#476	—	3	2	no	—
194	#476	—	3	1	no	—
195	#474	—	3	1	no	—
196	#446	C₃×D₃	1	1	yes	characteristic, complemented
197	#442	—	3	2	no	—
198	C₄×D₈	—	3	1	no	—
199	C₂×C₃×Q₈	—	2	1	no	—
200	C₂×C₃×Q₈	—	6	2	no	—
201	C₂×C₃×Q₈	—	6	1	no	—
202	C₂×C₃×Q₈	—	6	1	no	—
203	C₂×C₃×Q₈	—	12	4	no	—
204	C₂×C₃×Q₈	D₁₂	1	1	yes	characteristic
205	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
206	C₂×C₃×D₄	—	3	1	no	—
207	C₂×C₃×D₄	—	3	1	no	—
208	C₂²×C₃×C₄	—	6	1	no	—
209	C₂²×C₃×C₄	—	6	2	no	—
210	C₂²×C₃×C₄	—	6	1	no	—
211	C₂²×C₃×C₄	—	6	2	no	—
212	D₃×Q₈	—	4	4	no	—
213	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
214	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₄×D₃	—	2	1	no	—
216	C₂×C₄×D₃	—	2	2	no	—
217	C₂×C₄×D₃	—	2	1	no	—
218	C₂×C₄×D₃	—	2	2	no	—
219	C₂×Dic₆	—	2	2	no	—
220	C₂×Dic₆	—	2	1	no	—
221	C₂×Dic₆	—	2	1	no	—
222	C₃×D₈	—	3	4	no	—
223	C₂×C₃×C₈	—	2	1	no	—
224	C₂×C₃×C₈	—	2	1	no	—
225	C₂×C₃×C₈	—	2	2	no	—
226	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
227	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
228	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
229	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
230	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
231	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	2	2	no	—
234	C₃×C₄⋊C₄	—	3	2	no	—
235	C₃×C₄⋊C₄	—	3	1	no	—
236	C₃×C₄⋊C₄	—	3	2	no	—
237	C₃×C₄⋊C₄	—	3	1	no	—
238	C₃×C₄⋊C₄	—	6	2	no	—
239	C₃×C₄⋊C₄	—	6	2	no	—
240	C₃×C₄⋊C₄	—	6	1	no	—
241	C₃×C₄⋊C₄	—	6	1	no	—
242	C₃×C₄⋊C₄	—	6	2	no	—
243	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
244	C₃×C₄⋊C₄	D₁₂	1	2	yes	—
245	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
246	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
247	C₃×C₂²⋊C₄	—	6	1	no	—
248	C₃×C₂²⋊C₄	—	6	2	no	—
249	C₃×C₂²⋊C₄	—	6	1	no	—
250	C₃×C₂²⋊C₄	—	6	2	no	—
251	C₃×C₄²	—	2	1	no	—
252	C₃×C₄²	—	2	2	no	—
253	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
254	C₃×C₄²	C₂²×D₃	1	2	yes	—
255	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
256	C₃×C₄²	C₂³×C₃	1	2	yes	—
257	(C₂×D₃)⋊C₄	—	2	1	no	—
258	(C₂×D₃)⋊C₄	—	2	2	no	—
259	(C₂×D₃)⋊C₄	—	2	2	no	—
260	(C₂×D₃)⋊C₄	—	2	1	no	—
261	C₄⋊Dic₃	—	2	1	no	—
262	C₄⋊Dic₃	—	2	2	no	—
263	C₄⋊Dic₃	—	2	1	no	—
264	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
265	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
266	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
267	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
268	Dic₃⋊C₄	—	2	2	no	—
269	Dic₃⋊C₄	—	2	2	no	—
270	D₂₄	C₃×Q₈	1	4	yes	complemented
271	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₃×D₃	—	2	2	no	—
273	C₂×C₃×D₃	—	2	2	no	—
274	C₂×C₃×D₃	—	4	1	no	—
275	C₂×C₃×D₃	—	4	1	no	—
276	C₂×C₃×D₃	—	4	1	no	—
277	C₂×C₃×D₃	—	4	1	no	—
278	C₃²×C₄	—	2	2	no	—
279	C₃²×C₄	—	2	1	no	—
280	C₃²×C₄	—	2	2	no	—
281	C₃²×C₄	AGL(1,ℤ/8)	1	2	yes	—
282	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
283	C₃²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
284	C₃×Dic₃	—	4	1	no	—
285	C₃×Dic₃	—	4	2	no	—
286	C₃×Dic₃	—	4	1	no	—
287	C₃×Dic₃	—	4	2	no	—
288	C₂²×Q₈	—	6	1	no	—
289	C₂×D₈	—	3	1	no	—
290	C₄⋊Q₈	—	3	1	no	—
291	C₄⋊Q₈	—	3	2	no	—
292	C₄⋊Q₈	—	3	1	no	—
293	#125	—	3	2	no	—
294	C₂²⋊Q₈	—	6	1	no	—
295	C₂²⋊Q₈	—	6	1	no	—
296	C₂²⋊Q₈	—	6	2	no	—
297	C₂²⋊Q₈	—	6	2	no	—
298	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
299	C₄×D₄	—	3	1	no	—
300	C₄×D₄	—	3	2	no	—
301	C₄×D₄	—	3	1	no	—
302	C₄×D₄	—	3	2	no	—
303	C₂×C₄⋊C₄	—	6	1	no	—
304	#107	—	3	1	no	—
305	#107	—	3	2	no	—
306	#106	—	3	2	no	—
307	#106	—	3	2	no	—
308	#106	—	3	2	no	—
309	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
310	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
311	#102	—	3	1	no	—
312	#102	—	3	1	no	—
313	#102	—	3	2	no	—
314	#102	—	3	2	no	—
315	#97	C₂×C₃×D₃	1	2	yes	—
316	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
317	C₂³×C₃	—	6	1	no	—
318	C₂³×C₃	—	6	1	no	—
319	C₂²×D₃	—	2	1	no	—
320	C₂²×D₃	—	2	1	no	—
321	C₃×Q₈	—	2	2	no	—
322	C₃×Q₈	—	2	2	no	—
323	C₃×Q₈	—	4	2	no	—
324	C₃×Q₈	—	12	4	no	—
325	C₃×Q₈	—	12	2	no	—
326	C₃×Q₈	—	24	1	no	—
327	C₃×D₄	—	3	2	no	—
328	C₃×D₄	—	3	2	no	—
329	C₃×D₄	—	6	1	no	—
330	C₃×D₄	—	6	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	6	1	no	—
337	C₂×C₃×C₄	—	6	2	no	—
338	C₂×C₃×C₄	—	6	2	no	—
339	C₂×C₃×C₄	—	6	1	no	—
340	C₂×C₃×C₄	—	12	4	no	—
341	C₂×C₃×C₄	—	12	2	no	—
342	C₂×C₃×C₄	—	12	2	no	—
343	C₂×C₃×C₄	—	24	2	no	—
344	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
346	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
347	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
349	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
350	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
354	C₂×Dic₃	—	2	1	no	—
355	C₂×Dic₃	—	2	2	no	—
356	C₂×Dic₃	—	2	1	no	—
357	C₂×Dic₃	—	2	2	no	—
358	D₁₂	—	2	1	no	—
359	D₁₂	—	2	1	no	—
360	D₁₂	C₂×C₃×Q₈	1	2	yes	—
361	D₁₂	C₂×C₃×Q₈	1	2	yes	complemented
362	C₄×D₃	—	4	4	no	—
363	C₄×D₃	—	4	2	no	—
364	C₄×D₃	—	4	2	no	—
365	C₄×D₃	—	8	2	no	—
366	Dic₆	—	4	4	no	—
367	Dic₆	—	4	2	no	—
368	Dic₆	—	8	1	no	—
369	C₃×C₈	—	2	1	no	—
370	C₃×C₈	—	2	2	no	—
371	C₃×C₈	—	2	1	no	—
372	C₃×C₈	—	2	2	no	—
373	C₃×C₈	—	2	2	no	—
374	C₃×C₈	—	4	1	no	—
375	C₃×C₈	—	4	2	no	—
376	C₃×C₈	D₃×Q₈	1	2	yes	complemented
377	C₃×C₈	C₂×C₃×Q₈	1	2	yes	complemented
378	C₂×C₃²	D₄×Q₈	1	1	yes	characteristic
379	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
380	C₂×C₃²	#577	1	1	yes	characteristic
381	C₃×D₃	—	4	2	no	—
382	C₃×D₃	—	4	2	no	—
383	C₂×Q₈	—	6	2	no	—
384	C₂×Q₈	—	6	1	no	—
385	C₂×Q₈	—	6	1	no	—
386	C₂×Q₈	—	12	4	no	—
387	C₂×Q₈	C₃×D₁₂	1	1	yes	characteristic
388	C₂×D₄	—	3	1	no	—
389	C₂×D₄	—	3	1	no	—
390	C₂²×C₄	—	6	1	no	—
391	C₂²×C₄	—	6	2	no	—
392	C₂²×C₄	—	6	1	no	—
393	C₂²×C₄	—	6	2	no	—
394	D₈	—	3	4	no	—
395	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
396	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
397	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
398	C₄⋊C₄	—	3	2	no	—
399	C₄⋊C₄	—	3	1	no	—
400	C₄⋊C₄	—	3	2	no	—
401	C₄⋊C₄	—	3	1	no	—
402	C₄⋊C₄	—	6	2	no	—
403	C₄⋊C₄	—	6	1	no	—
404	C₄⋊C₄	—	6	2	no	—
405	C₄⋊C₄	—	6	1	no	—
406	C₄⋊C₄	—	6	2	no	—
407	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
408	C₄⋊C₄	C₃×D₁₂	1	2	yes	—
409	C₂²⋊C₄	—	6	1	no	—
410	C₂²⋊C₄	—	6	2	no	—
411	C₂²⋊C₄	—	6	1	no	—
412	C₂²⋊C₄	—	6	2	no	—
413	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
414	C₄²	C₂²×C₃×D₃	1	2	yes	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	6	2	no	—
417	C₂²×C₃	—	6	2	no	—
418	C₂²×C₃	—	12	1	no	—
419	C₂²×C₃	—	12	1	no	—
420	C₂²×C₃	—	12	1	no	—
421	C₂²×C₃	—	12	1	no	—
422	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
423	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
424	C₂×D₃	—	2	2	no	—
425	C₂×D₃	—	2	2	no	—
426	C₂×D₃	—	4	1	no	—
427	C₂×D₃	—	4	1	no	—
428	C₂×D₃	—	4	1	no	—
429	C₂×D₃	—	4	1	no	—
430	C₃×C₄	—	2	2	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	2	1	no	—
436	C₃×C₄	—	2	2	no	—
437	C₃×C₄	—	2	1	no	—
438	C₃×C₄	—	2	1	no	—
439	C₃×C₄	—	4	2	no	—
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	12	2	no	—
443	C₃×C₄	—	12	1	no	—
444	C₃×C₄	—	12	1	no	—
445	C₃×C₄	—	12	2	no	—
446	C₃×C₄	#908	1	2	yes	—
447	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
448	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
449	C₃×C₄	#1010	1	1	yes	characteristic
450	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
451	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
452	Dic₃	—	4	1	no	—
453	Dic₃	—	4	2	no	—
454	Dic₃	—	4	1	no	—
455	Dic₃	—	4	2	no	—
456	C₃²	#3384	1	1	yes	characteristic, complemented, Sylow
457	C₂³	—	6	1	no	—
458	C₂³	—	6	1	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	12	4	no	—
461	Q₈	—	12	2	no	—
462	Q₈	—	24	1	no	—
463	D₄	—	3	2	no	—
464	D₄	—	3	2	no	—
465	D₄	—	6	1	no	—
466	D₄	—	6	1	no	—
467	C₂×C₄	—	6	1	no	—
468	C₂×C₄	—	6	2	no	—
469	C₂×C₄	—	6	2	no	—
470	C₂×C₄	—	6	1	no	—
471	C₂×C₄	—	12	4	no	—
472	C₂×C₄	—	12	2	no	—
473	C₂×C₄	—	12	2	no	—
474	C₂×C₄	—	24	2	no	—
475	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
476	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
477	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
478	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
479	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
480	C₈	—	2	1	no	—
481	C₈	—	2	2	no	—
482	C₈	C₃×D₃×Q₈	1	2	yes	complemented
483	C₂×C₃	—	2	1	no	—
484	C₂×C₃	—	2	1	no	—
485	C₂×C₃	—	2	1	no	—
486	C₂×C₃	—	12	2	no	—
487	C₂×C₃	—	12	2	no	—
488	C₂×C₃	Q₈×D₁₂	1	1	yes	characteristic
489	C₂×C₃	C₂×#908	1	1	yes	characteristic
490	C₂×C₃	#5751	1	1	yes	characteristic
491	C₂×C₃	C₃×D₄×Q₈	1	1	yes	characteristic
492	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
493	C₂×C₃	C₃×#577	1	1	yes	characteristic
494	D₃	—	4	2	no	—
495	D₃	—	4	2	no	—
496	C₂²	—	6	2	no	—
497	C₂²	—	6	2	no	—
498	C₂²	—	12	1	no	—
499	C₂²	—	12	1	no	—
500	C₂²	—	12	1	no	—
501	C₂²	—	12	1	no	—
502	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	1	no	—
506	C₄	—	12	2	no	—
507	C₄	—	12	1	no	—
508	C₄	—	12	1	no	—
509	C₄	—	12	2	no	—
510	C₄	C₃×#908	1	2	yes	—
511	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
512	C₄	C₃×#1010	1	1	yes	characteristic
513	C₃	—	2	1	no	—
514	C₃	#79975	1	1	yes	characteristic, direct product factor
515	C₃	C₃×#3384	1	1	yes	characteristic, complemented
516	C₂	—	12	2	no	—
517	C₂	—	12	2	no	—
518	C₂	C₃×Q₈×D₁₂	1	1	yes	characteristic
519	C₂	C₂×C₃×#908	1	1	yes	characteristic
520	C₂	C₃×#5751	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#446	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×D₂₄	C₂²
hypercenter	C₃×#446	D₃
hypocenter	C₃	C₃×#3384
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈ ◁ C₃×#446

Complements

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

N	H ≅ G/N	type
1. C₃×#5579	C₂	semidirect
2. C₃×Q₈×D₁₂	C₂	semidirect
3. C₃²×#446	C₂	semidirect
4. C₃×#4847	C₂	semidirect
5. C₃×#4846	C₂	semidirect
6. C₃×#4842	C₂	semidirect
7. C₃×#4842	C₂	semidirect
9. C₃×#4702	C₂	semidirect
11. C₃×#4680	C₂	semidirect
13. #79975	C₃	direct (N × H)
45. #5579	C₂×C₃	semidirect
46. Q₈×D₁₂	C₂×C₃	semidirect
54. C₃×#446	D₃	semidirect
55. C₃×#446	C₂×C₃	semidirect
58. #4847	C₂×C₃	semidirect
59. #4846	C₂×C₃	semidirect
60. #4842	C₂×C₃	semidirect
61. #4842	C₂×C₃	semidirect
63. #4702	C₂×C₃	semidirect
65. #4680	C₂×C₃	semidirect
97. C₃×D₂₄	Q₈	semidirect
177. C₃×D₁₂	C₂×Q₈	semidirect
187. C₃²×C₈	C₂×Q₈	semidirect
196. #446	C₃×D₃	semidirect
270. D₂₄	C₃×Q₈	semidirect
361. D₁₂	C₂×C₃×Q₈	semidirect
376. C₃×C₈	D₃×Q₈	semidirect
377. C₃×C₈	C₂×C₃×Q₈	semidirect
456. C₃²	#3384	semidirect
482. C₈	C₃×D₃×Q₈	semidirect
514. C₃	#79975	direct (N × H)
515. C₃	C₃×#3384	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5579	2
C₃×Q₈×D₁₂	2
C₃²×#446	2
C₃×#4847	2
C₃×#4846	2
C₃×#4842	2
C₃×#4711	2
C₃×#4702	2
C₃×C₄×D₂₄	2
C₃×#4680	2
C₃×#3384	3
#79975	3

Subgroups — C3×#79975 #11897525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79975 #11897525