Subgroups — C₃²×#3045 #11770094

Order 1152.

1512 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#464	C₂	1	2	yes	maximal, complemented
6	C₃²×#463	C₂	1	2	yes	maximal, complemented
7	C₃²×#460	C₂	1	2	yes	maximal, complemented
8	C₃²×#459	C₂	1	2	yes	maximal, complemented
9	C₃²×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#417	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃²×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3045	C₃	1	4	yes	maximal, direct product factor
13	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
16	C₃²×AGL(1,ℤ/8)	—	2	4	no	—
17	C₃²×#135	—	2	4	no	—
18	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
20	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃²×D₈	C₂²	1	2	yes	—
23	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
26	C₃²×#127	C₂²	1	2	yes	—
27	C₃²×#124	C₂²	1	2	yes	—
28	C₃²×#121	—	2	1	no	—
29	C₃²×#121	—	2	1	no	—
30	C₃²×#120	—	2	2	no	—
31	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
32	C₃²×C₄×D₄	—	2	2	no	—
33	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
34	C₃²×#117	—	2	1	no	—
35	C₃²×#117	C₂²	1	1	yes	characteristic
36	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
37	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
39	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₃²×#103	C₂²	1	2	yes	complemented
41	C₃²×#102	C₂²	1	2	yes	—
42	C₃²×#102	C₂²	1	2	yes	—
43	C₃²×#102	C₂²	1	2	yes	complemented
44	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	4	yes	complemented
45	C₂×C₃×#135	C₂×C₃	1	4	yes	complemented
46	C₃×#535	C₂×C₃	1	4	yes	complemented
47	C₃×#520	C₂×C₃	1	4	yes	complemented
48	C₃×#464	C₂×C₃	1	8	yes	complemented
49	C₃×#463	C₂×C₃	1	8	yes	complemented
50	C₃×#460	C₂×C₃	1	8	yes	complemented
51	C₃×#459	C₂×C₃	1	8	yes	complemented
52	C₃×#424	C₂×C₃	1	4	yes	complemented
53	C₃×#417	C₂×C₃	1	4	yes	complemented
54	C₂×C₃×#102	C₂×C₃	1	4	yes	complemented
55	C₂⁴×C₃²	—	2	1	no	—
56	C₃²×#41	—	2	2	no	—
57	C₃²×#41	—	2	2	no	—
58	C₃²×#41	—	2	2	no	—
59	C₃²×#41	D₄	1	4	yes	complemented
60	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
62	C₂×C₃²×D₄	—	2	1	no	—
63	C₂×C₃²×D₄	—	2	1	no	—
64	C₂×C₃²×D₄	—	2	2	no	—
65	C₂×C₃²×D₄	—	2	1	no	—
66	C₂×C₃²×D₄	—	2	2	no	—
67	C₂×C₃²×D₄	—	2	2	no	—
68	C₂×C₃²×D₄	—	2	2	no	—
69	C₂×C₃²×D₄	C₂³	1	2	yes	—
70	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
71	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
72	C₂²×C₃²×C₄	—	2	1	no	—
73	C₂²×C₃²×C₄	—	2	1	no	—
74	C₂²×C₃²×C₄	—	2	1	no	—
75	C₂²×C₃²×C₄	—	2	2	no	—
76	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
77	C₃²×Q₁₆	—	2	2	no	—
78	C₃²×SD₁₆	—	2	4	no	—
79	C₃²×SD₁₆	—	2	2	no	—
80	C₃²×SD₁₆	—	2	2	no	—
81	C₃²×D₈	—	2	4	no	—
82	C₃²×D₈	—	2	2	no	—
83	C₃²×M₁₆	—	2	2	no	—
84	C₂×C₃²×C₈	—	2	2	no	—
85	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
87	C₂×C₃²×C₈	C₂³	1	2	yes	—
88	C₃²×C₄⋊C₄	—	2	1	no	—
89	C₃²×C₄⋊C₄	—	2	2	no	—
90	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
92	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
93	C₃²×C₂²⋊C₄	—	2	2	no	—
94	C₃²×C₂²⋊C₄	—	2	2	no	—
95	C₃²×C₂²⋊C₄	—	2	2	no	—
96	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
97	C₃²×C₄²	—	2	2	no	—
98	C₃²×C₄²	C₂³	1	2	yes	—
99	#3045	C₃²	1	1	yes	characteristic, direct product factor, Sylow
100	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
101	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
102	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
103	C₃×AGL(1,ℤ/8)	—	2	16	no	—
104	C₃×#135	—	2	16	no	—
105	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	complemented
106	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
107	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	complemented
108	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	complemented
109	C₂×C₃×D₈	C₂²×C₃	1	8	yes	—
110	C₂×C₃×D₈	C₂²×C₃	1	4	yes	complemented
111	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
112	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
113	C₃×#127	C₂²×C₃	1	8	yes	—
114	C₃×#124	C₂²×C₃	1	8	yes	—
115	C₃×#121	—	2	4	no	—
116	C₃×#121	—	2	4	no	—
117	C₃×#120	—	2	8	no	—
118	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	complemented
119	C₃×C₄×D₄	—	2	8	no	—
120	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
121	C₃×#117	—	2	4	no	—
122	C₃×#117	C₂²×C₃	1	4	yes	—
123	C₂×C₃×C₄⋊C₄	—	2	4	no	—
124	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
125	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
126	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
127	C₃×#103	C₂²×C₃	1	8	yes	complemented
128	C₃×#102	C₂²×C₃	1	8	yes	—
129	C₃×#102	C₂²×C₃	1	8	yes	—
130	C₃×#102	C₂²×C₃	1	8	yes	complemented
131	C₂³×C₃²	—	2	1	no	—
132	C₂³×C₃²	—	2	2	no	—
133	C₂³×C₃²	—	2	1	no	—
134	C₂³×C₃²	—	4	2	no	—
135	C₂³×C₃²	—	8	1	no	—
136	C₂³×C₃²	—	8	1	no	—
137	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
138	C₃²×Q₈	—	2	1	no	—
139	C₃²×Q₈	—	2	1	no	—
140	C₃²×Q₈	—	2	1	no	—
141	C₃²×Q₈	C₂×D₄	1	2	yes	—
142	C₃²×D₄	—	2	4	no	—
143	C₃²×D₄	—	2	2	no	—
144	C₃²×D₄	—	2	1	no	—
145	C₃²×D₄	—	2	1	no	—
146	C₃²×D₄	—	2	2	no	—
147	C₃²×D₄	—	2	1	no	—
148	C₃²×D₄	—	4	2	no	—
149	C₃²×D₄	—	4	2	no	—
150	C₃²×D₄	—	8	2	no	—
151	C₃²×D₄	—	8	2	no	—
152	C₃²×D₄	C₂×D₄	1	2	yes	—
153	C₂×C₃²×C₄	—	2	1	no	—
154	C₂×C₃²×C₄	—	2	4	no	—
155	C₂×C₃²×C₄	—	2	2	no	—
156	C₂×C₃²×C₄	—	2	1	no	—
157	C₂×C₃²×C₄	—	4	2	no	—
158	C₂×C₃²×C₄	—	8	2	no	—
159	C₂×C₃²×C₄	—	8	1	no	—
160	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
161	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
162	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
164	C₂×C₃²×C₄	#41	1	2	yes	—
165	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
166	C₃²×C₈	—	2	1	no	—
167	C₃²×C₈	—	2	1	no	—
168	C₃²×C₈	—	2	2	no	—
169	C₂×AGL(1,ℤ/8)	C₂×C₃²	1	1	yes	characteristic, complemented
170	C₂×#135	C₂×C₃²	1	1	yes	characteristic, complemented
171	#535	C₂×C₃²	1	1	yes	characteristic, complemented
172	#520	C₂×C₃²	1	1	yes	characteristic, complemented
173	#464	C₂×C₃²	1	2	yes	complemented
174	#463	C₂×C₃²	1	2	yes	complemented
175	#460	C₂×C₃²	1	2	yes	complemented
176	#459	C₂×C₃²	1	2	yes	complemented
177	#424	C₂×C₃²	1	1	yes	characteristic, complemented
178	#417	C₂×C₃²	1	1	yes	characteristic, complemented
179	C₂×#102	C₂×C₃²	1	1	yes	characteristic, complemented
180	C₂⁴×C₃	—	2	4	no	—
181	C₃×#41	—	2	8	no	—
182	C₃×#41	—	2	8	no	—
183	C₃×#41	—	2	8	no	—
184	C₃×#41	C₃×D₄	1	16	yes	complemented
185	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
186	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
187	C₂×C₃×D₄	—	2	4	no	—
188	C₂×C₃×D₄	—	2	4	no	—
189	C₂×C₃×D₄	—	2	8	no	—
190	C₂×C₃×D₄	—	2	4	no	—
191	C₂×C₃×D₄	—	2	8	no	—
192	C₂×C₃×D₄	—	2	8	no	—
193	C₂×C₃×D₄	—	2	8	no	—
194	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
195	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
196	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
197	C₂²×C₃×C₄	—	2	4	no	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	—	2	8	no	—
201	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
202	C₃×Q₁₆	—	2	8	no	—
203	C₃×SD₁₆	—	2	16	no	—
204	C₃×SD₁₆	—	2	8	no	—
205	C₃×SD₁₆	—	2	8	no	—
206	C₃×D₈	—	2	16	no	—
207	C₃×D₈	—	2	8	no	—
208	C₃×M₁₆	—	2	8	no	—
209	C₂×C₃×C₈	—	2	8	no	—
210	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
211	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
212	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
213	C₃×C₄⋊C₄	—	2	4	no	—
214	C₃×C₄⋊C₄	—	2	8	no	—
215	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
216	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
217	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
218	C₃×C₂²⋊C₄	—	2	8	no	—
219	C₃×C₂²⋊C₄	—	2	8	no	—
220	C₃×C₂²⋊C₄	—	2	8	no	—
221	C₃×C₂²⋊C₄	C₃×D₄	1	8	yes	—
222	C₃×C₄²	—	2	8	no	—
223	C₃×C₄²	C₂³×C₃	1	8	yes	—
224	C₂²×C₃²	—	2	1	no	—
225	C₂²×C₃²	—	2	1	no	—
226	C₂²×C₃²	—	2	2	no	—
227	C₂²×C₃²	—	4	1	no	—
228	C₂²×C₃²	—	4	1	no	—
229	C₂²×C₃²	—	4	1	no	—
230	C₂²×C₃²	—	4	2	no	—
231	C₂²×C₃²	—	4	1	no	—
232	C₂²×C₃²	—	4	2	no	—
233	C₂²×C₃²	—	4	1	no	—
234	C₂²×C₃²	—	4	2	no	—
235	C₂²×C₃²	—	8	4	no	—
236	C₂²×C₃²	#121	1	2	yes	—
237	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
238	C₃²×C₄	—	2	2	no	—
239	C₃²×C₄	—	2	2	no	—
240	C₃²×C₄	—	2	2	no	—
241	C₃²×C₄	—	4	1	no	—
242	C₃²×C₄	—	4	2	no	—
243	C₃²×C₄	#121	1	2	yes	—
244	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
245	C₃²×C₄	C₂×#41	1	1	yes	characteristic
246	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
247	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
248	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
249	AGL(1,ℤ/8)	—	2	4	no	—
250	#135	—	2	4	no	—
251	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic, complemented
252	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
253	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic, complemented
254	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic, complemented
255	C₂×D₈	C₂²×C₃²	1	2	yes	—
256	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic, complemented
257	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
258	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
259	#127	C₂²×C₃²	1	2	yes	—
260	#124	C₂²×C₃²	1	2	yes	—
261	#121	—	2	1	no	—
262	#121	—	2	1	no	—
263	#120	—	2	2	no	—
264	C₄×Q₈	C₂²×C₃²	1	2	yes	complemented
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
267	#117	—	2	1	no	—
268	#117	C₂²×C₃²	1	1	yes	characteristic
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
271	C₄⋊C₈	C₂²×C₃²	1	2	yes	complemented
272	C₄⋊C₈	C₂²×C₃²	1	2	yes	complemented
273	#103	C₂²×C₃²	1	2	yes	complemented
274	#102	C₂²×C₃²	1	2	yes	—
275	#102	C₂²×C₃²	1	2	yes	—
276	#102	C₂²×C₃²	1	2	yes	complemented
277	C₂³×C₃	—	2	4	no	—
278	C₂³×C₃	—	2	8	no	—
279	C₂³×C₃	—	2	4	no	—
280	C₂³×C₃	—	4	8	no	—
281	C₂³×C₃	—	8	4	no	—
282	C₂³×C₃	—	8	4	no	—
283	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
284	C₃×Q₈	—	2	4	no	—
285	C₃×Q₈	—	2	4	no	—
286	C₃×Q₈	—	2	4	no	—
287	C₃×Q₈	C₂×C₃×D₄	1	8	yes	—
288	C₃×D₄	—	2	16	no	—
289	C₃×D₄	—	2	8	no	—
290	C₃×D₄	—	2	4	no	—
291	C₃×D₄	—	2	4	no	—
292	C₃×D₄	—	2	8	no	—
293	C₃×D₄	—	2	4	no	—
294	C₃×D₄	—	4	8	no	—
295	C₃×D₄	—	4	8	no	—
296	C₃×D₄	—	8	8	no	—
297	C₃×D₄	—	8	8	no	—
298	C₃×D₄	C₂×C₃×D₄	1	8	yes	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	—	2	16	no	—
301	C₂×C₃×C₄	—	2	8	no	—
302	C₂×C₃×C₄	—	2	4	no	—
303	C₂×C₃×C₄	—	4	8	no	—
304	C₂×C₃×C₄	—	8	8	no	—
305	C₂×C₃×C₄	—	8	4	no	—
306	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
307	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
308	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
309	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
310	C₂×C₃×C₄	C₃×#41	1	8	yes	—
311	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
312	C₃×C₈	—	2	4	no	—
313	C₃×C₈	—	2	4	no	—
314	C₃×C₈	—	2	8	no	—
315	C₂×C₃²	—	2	2	no	—
316	C₂×C₃²	—	4	2	no	—
317	C₂×C₃²	—	8	1	no	—
318	C₂×C₃²	—	8	2	no	—
319	C₂×C₃²	C₂×#121	1	1	yes	characteristic
320	C₂×C₃²	#576	1	1	yes	characteristic
321	C₂×C₃²	#577	1	1	yes	characteristic
322	C₂⁴	—	2	1	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	C₃²×D₄	1	4	yes	complemented
327	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
328	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂³×C₃²	1	2	yes	—
337	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
338	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
344	Q₁₆	—	2	2	no	—
345	SD₁₆	—	2	4	no	—
346	SD₁₆	—	2	2	no	—
347	SD₁₆	—	2	2	no	—
348	D₈	—	2	4	no	—
349	D₈	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
353	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
354	C₂×C₈	C₂³×C₃²	1	2	yes	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
358	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
359	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	C₃²×D₄	1	2	yes	—
364	C₄²	—	2	2	no	—
365	C₄²	C₂³×C₃²	1	2	yes	—
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	2	8	no	—
369	C₂²×C₃	—	4	4	no	—
370	C₂²×C₃	—	4	4	no	—
371	C₂²×C₃	—	4	4	no	—
372	C₂²×C₃	—	4	8	no	—
373	C₂²×C₃	—	4	4	no	—
374	C₂²×C₃	—	4	8	no	—
375	C₂²×C₃	—	4	4	no	—
376	C₂²×C₃	—	4	8	no	—
377	C₂²×C₃	—	8	16	no	—
378	C₂²×C₃	C₃×#121	1	8	yes	—
379	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
380	C₃×C₄	—	2	8	no	—
381	C₃×C₄	—	2	8	no	—
382	C₃×C₄	—	2	8	no	—
383	C₃×C₄	—	4	8	no	—
384	C₃×C₄	—	4	4	no	—
385	C₃×C₄	C₃×#121	1	8	yes	—
386	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
387	C₃×C₄	C₂×C₃×#41	1	4	yes	—
388	C₃²	#3045	1	1	yes	characteristic, direct product factor, Sylow
389	C₂³	—	2	1	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	1	no	—
394	C₂³	—	8	1	no	—
395	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
396	Q₈	—	2	1	no	—
397	Q₈	—	2	1	no	—
398	Q₈	—	2	1	no	—
399	Q₈	C₂×C₃²×D₄	1	2	yes	—
400	D₄	—	2	4	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	1	no	—
403	D₄	—	2	1	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	1	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	8	2	no	—
409	D₄	—	8	2	no	—
410	D₄	C₂×C₃²×D₄	1	2	yes	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	—	8	1	no	—
418	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
419	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
420	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
421	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
422	C₂×C₄	C₃²×#41	1	2	yes	—
423	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	—	2	2	no	—
427	C₂×C₃	—	2	8	no	—
428	C₂×C₃	—	4	8	no	—
429	C₂×C₃	—	8	8	no	—
430	C₂×C₃	—	8	4	no	—
431	C₂×C₃	C₂×C₃×#121	1	4	yes	—
432	C₂×C₃	C₃×#576	1	4	yes	—
433	C₂×C₃	C₃×#577	1	4	yes	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	4	no	—
446	C₂²	C₃²×#121	1	2	yes	—
447	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	C₃²×#121	1	2	yes	—
454	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
455	C₄	C₂×C₃²×#41	1	1	yes	characteristic
456	C₃	C₃×#3045	1	4	yes	direct product factor
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	8	2	no	—
460	C₂	—	8	1	no	—
461	C₂	C₂×C₃²×#121	1	1	yes	characteristic
462	C₂	C₃²×#576	1	1	yes	characteristic
463	C₂	C₃²×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₃²×#135	C₂	semidirect
3. C₃²×#535	C₂	semidirect
4. C₃²×#520	C₂	semidirect
5. C₃²×#464	C₂	semidirect
6. C₃²×#463	C₂	semidirect
7. C₃²×#460	C₂	semidirect
8. C₃²×#459	C₂	semidirect
9. C₃²×#424	C₂	semidirect
10. C₃²×#417	C₂	semidirect
11. C₂×C₃²×#102	C₂	semidirect
12. C₃×#3045	C₃	direct (N × H)
18. C₂×C₃²×Q₁₆	C₂²	semidirect
20. C₂×C₃²×SD₁₆	C₂²	semidirect
21. C₂×C₃²×SD₁₆	C₂²	semidirect
23. C₂×C₃²×D₈	C₂²	semidirect
31. C₃²×C₄×Q₈	C₂²	semidirect
33. C₃²×C₄×D₄	C₂²	semidirect
38. C₃²×C₄⋊C₈	C₂²	semidirect
39. C₃²×C₄⋊C₈	C₂²	semidirect
40. C₃²×#103	C₂²	semidirect
43. C₃²×#102	C₂²	semidirect
44. C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	semidirect
45. C₂×C₃×#135	C₂×C₃	semidirect
46. C₃×#535	C₂×C₃	semidirect
47. C₃×#520	C₂×C₃	semidirect
48. C₃×#464	C₂×C₃	semidirect
49. C₃×#463	C₂×C₃	semidirect
50. C₃×#460	C₂×C₃	semidirect
51. C₃×#459	C₂×C₃	semidirect
52. C₃×#424	C₂×C₃	semidirect
53. C₃×#417	C₂×C₃	semidirect
54. C₂×C₃×#102	C₂×C₃	semidirect
59. C₃²×#41	D₄	semidirect
99. #3045	C₃²	direct (N × H)
105. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
107. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
108. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
110. C₂×C₃×D₈	C₂²×C₃	semidirect
118. C₃×C₄×Q₈	C₂²×C₃	semidirect
120. C₃×C₄×D₄	C₂²×C₃	semidirect
125. C₃×C₄⋊C₈	C₂²×C₃	semidirect
126. C₃×C₄⋊C₈	C₂²×C₃	semidirect
127. C₃×#103	C₂²×C₃	semidirect
130. C₃×#102	C₂²×C₃	semidirect
169. C₂×AGL(1,ℤ/8)	C₂×C₃²	semidirect
170. C₂×#135	C₂×C₃²	semidirect
171. #535	C₂×C₃²	semidirect
172. #520	C₂×C₃²	semidirect
173. #464	C₂×C₃²	semidirect
174. #463	C₂×C₃²	semidirect
175. #460	C₂×C₃²	semidirect
176. #459	C₂×C₃²	semidirect
177. #424	C₂×C₃²	semidirect
178. #417	C₂×C₃²	semidirect
179. C₂×#102	C₂×C₃²	semidirect
184. C₃×#41	C₃×D₄	semidirect
251. C₂×Q₁₆	C₂²×C₃²	semidirect
253. C₂×SD₁₆	C₂²×C₃²	semidirect
254. C₂×SD₁₆	C₂²×C₃²	semidirect
256. C₂×D₈	C₂²×C₃²	semidirect
264. C₄×Q₈	C₂²×C₃²	semidirect
266. C₄×D₄	C₂²×C₃²	semidirect
271. C₄⋊C₈	C₂²×C₃²	semidirect
272. C₄⋊C₈	C₂²×C₃²	semidirect
273. #103	C₂²×C₃²	semidirect
276. #102	C₂²×C₃²	semidirect
326. #41	C₃²×D₄	semidirect
388. C₃²	#3045	direct (N × H)
456. C₃	C₃×#3045	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×AGL(1,ℤ/8)	2
C₂×C₃²×#135	2
C₃²×#535	2
C₃²×#520	2
C₃²×#464	2
C₃²×#463	2
C₃²×#460	2
C₃²×#459	2
C₃²×#424	2
C₃²×#417	2
C₂×C₃²×#102	2
C₃×#3045	3

Subgroups — C32×#3045 #11770094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3045 #11770094