Subgroups — C₃²×#3062 #11770111

Order 1152.

1512 conjugacy classes of subgroups.

The subgroup lattice has 456 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×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#537	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#535	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#469	C₂	1	2	yes	maximal, complemented
6	C₃²×#468	C₂	1	2	yes	maximal, complemented
7	C₃²×#466	C₂	1	2	yes	maximal, complemented
8	C₃²×#465	C₂	1	2	yes	maximal, complemented
9	C₃²×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃²×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3062	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	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃²×D₈	C₂²	1	2	yes	—
19	C₃²×#131	—	2	4	no	—
20	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃²×M₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
23	C₂²×C₃²×C₈	C₂²	1	2	yes	complemented
24	C₃²×#127	—	2	1	no	—
25	C₃²×#124	—	2	1	no	—
26	C₃²×C₂²⋊Q₈	—	2	1	no	—
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₃²×#121	—	2	1	no	—
29	C₃²×#121	—	2	2	no	—
30	C₃²×#121	C₂²	1	2	yes	—
31	C₃²×#121	C₂²	1	2	yes	—
32	C₃²×#121	C₂²	1	2	yes	complemented
33	C₃²×#120	—	2	2	no	—
34	C₃²×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₃²×#107	C₂²	1	2	yes	complemented
37	C₃²×#106	C₂²	1	2	yes	complemented
38	C₃²×#103	C₂²	1	1	yes	characteristic, complemented
39	C₃²×#103	C₂²	1	1	yes	characteristic, complemented
40	C₃²×#102	C₂²	1	2	yes	—
41	C₃²×#102	C₂²	1	2	yes	—
42	C₃²×#102	C₂²	1	1	yes	characteristic, complemented
43	C₃²×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	4	yes	complemented
45	C₂×C₃×#131	C₂×C₃	1	4	yes	complemented
46	C₃×#537	C₂×C₃	1	4	yes	complemented
47	C₃×#535	C₂×C₃	1	4	yes	complemented
48	C₃×#469	C₂×C₃	1	8	yes	complemented
49	C₃×#468	C₂×C₃	1	8	yes	complemented
50	C₃×#466	C₂×C₃	1	8	yes	complemented
51	C₃×#465	C₂×C₃	1	8	yes	complemented
52	C₃×#428	C₂×C₃	1	4	yes	complemented
53	C₃×#416	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	—	2	2	no	—
60	C₂×C₃²×Q₈	D₄	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	2	no	—
64	C₂×C₃²×D₄	—	2	2	no	—
65	C₂×C₃²×D₄	—	2	2	no	—
66	C₂×C₃²×D₄	—	2	2	no	—
67	C₂×C₃²×D₄	—	2	1	no	—
68	C₂×C₃²×D₄	—	2	2	no	—
69	C₂×C₃²×D₄	D₄	1	2	yes	—
70	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
71	C₂×C₃²×D₄	C₂³	1	2	yes	—
72	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
73	C₂²×C₃²×C₄	—	2	1	no	—
74	C₂²×C₃²×C₄	—	2	1	no	—
75	C₂²×C₃²×C₄	C₂³	1	2	yes	—
76	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
77	C₃²×SD₁₆	—	2	4	no	—
78	C₃²×D₈	—	2	4	no	—
79	C₃²×M₁₆	—	2	4	no	—
80	C₃²×M₁₆	D₄	1	4	yes	complemented
81	C₂×C₃²×C₈	—	2	2	no	—
82	C₂×C₃²×C₈	—	2	4	no	—
83	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₃²×C₈	C₂³	1	2	yes	—
86	C₃²×C₄⋊C₄	—	2	1	no	—
87	C₃²×C₄⋊C₄	—	2	2	no	—
88	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
89	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₃²×C₂²⋊C₄	—	2	1	no	—
92	C₃²×C₂²⋊C₄	—	2	2	no	—
93	C₃²×C₂²⋊C₄	—	2	2	no	—
94	C₃²×C₂²⋊C₄	—	2	2	no	—
95	C₃²×C₂²⋊C₄	—	2	2	no	—
96	C₃²×C₄²	—	2	1	no	—
97	#3062	C₃²	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
99	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
100	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
101	C₃×AGL(1,ℤ/8)	—	2	16	no	—
102	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
103	C₂×C₃×D₈	C₂²×C₃	1	8	yes	—
104	C₃×#131	—	2	16	no	—
105	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
106	C₂×C₃×M₁₆	C₂²×C₃	1	8	yes	complemented
107	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
108	C₂²×C₃×C₈	C₂²×C₃	1	8	yes	complemented
109	C₃×#127	—	2	4	no	—
110	C₃×#124	—	2	4	no	—
111	C₃×C₂²⋊Q₈	—	2	4	no	—
112	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
113	C₃×#121	—	2	4	no	—
114	C₃×#121	—	2	8	no	—
115	C₃×#121	C₂²×C₃	1	8	yes	—
116	C₃×#121	C₂²×C₃	1	8	yes	—
117	C₃×#121	C₂²×C₃	1	8	yes	complemented
118	C₃×#120	—	2	8	no	—
119	C₃×#117	C₂²×C₃	1	4	yes	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
121	C₃×#107	C₂²×C₃	1	8	yes	complemented
122	C₃×#106	C₂²×C₃	1	8	yes	complemented
123	C₃×#103	C₂²×C₃	1	4	yes	complemented
124	C₃×#103	C₂²×C₃	1	4	yes	complemented
125	C₃×#102	C₂²×C₃	1	8	yes	—
126	C₃×#102	C₂²×C₃	1	8	yes	—
127	C₃×#102	C₂²×C₃	1	4	yes	complemented
128	C₃×#102	C₂²×C₃	1	4	yes	complemented
129	C₂³×C₃²	—	2	2	no	—
130	C₂³×C₃²	—	2	1	no	—
131	C₂³×C₃²	—	4	2	no	—
132	C₂³×C₃²	—	8	1	no	—
133	C₂³×C₃²	—	8	1	no	—
134	C₂³×C₃²	C₂×D₄	1	2	yes	—
135	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
136	C₃²×Q₈	—	2	2	no	—
137	C₃²×Q₈	—	2	1	no	—
138	C₃²×Q₈	—	2	1	no	—
139	C₃²×D₄	—	2	4	no	—
140	C₃²×D₄	—	2	2	no	—
141	C₃²×D₄	—	2	1	no	—
142	C₃²×D₄	—	2	2	no	—
143	C₃²×D₄	—	2	2	no	—
144	C₃²×D₄	—	2	1	no	—
145	C₃²×D₄	—	4	2	no	—
146	C₃²×D₄	—	4	2	no	—
147	C₃²×D₄	—	8	2	no	—
148	C₃²×D₄	—	8	2	no	—
149	C₃²×D₄	—	8	2	no	—
150	C₂×C₃²×C₄	—	2	2	no	—
151	C₂×C₃²×C₄	—	2	2	no	—
152	C₂×C₃²×C₄	—	2	1	no	—
153	C₂×C₃²×C₄	—	2	1	no	—
154	C₂×C₃²×C₄	—	2	2	no	—
155	C₂×C₃²×C₄	—	2	1	no	—
156	C₂×C₃²×C₄	—	4	2	no	—
157	C₂×C₃²×C₄	—	8	1	no	—
158	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
159	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
161	C₂×C₃²×C₄	#41	1	2	yes	—
162	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
163	C₃²×C₈	—	2	1	no	—
164	C₃²×C₈	—	2	1	no	—
165	C₃²×C₈	C₂×D₄	1	4	yes	—
166	C₂×AGL(1,ℤ/8)	C₂×C₃²	1	1	yes	characteristic, complemented
167	C₂×#131	C₂×C₃²	1	1	yes	characteristic, complemented
168	#537	C₂×C₃²	1	1	yes	characteristic, complemented
169	#535	C₂×C₃²	1	1	yes	characteristic, complemented
170	#469	C₂×C₃²	1	2	yes	complemented
171	#468	C₂×C₃²	1	2	yes	complemented
172	#466	C₂×C₃²	1	2	yes	complemented
173	#465	C₂×C₃²	1	2	yes	complemented
174	#428	C₂×C₃²	1	1	yes	characteristic, complemented
175	#416	C₂×C₃²	1	1	yes	characteristic, complemented
176	C₂×#102	C₂×C₃²	1	1	yes	characteristic, complemented
177	C₂⁴×C₃	—	2	4	no	—
178	C₃×#41	—	2	8	no	—
179	C₃×#41	—	2	8	no	—
180	C₃×#41	—	2	8	no	—
181	C₃×#41	—	2	8	no	—
182	C₂×C₃×Q₈	C₃×D₄	1	4	yes	—
183	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
184	C₂×C₃×D₄	—	2	4	no	—
185	C₂×C₃×D₄	—	2	8	no	—
186	C₂×C₃×D₄	—	2	8	no	—
187	C₂×C₃×D₄	—	2	8	no	—
188	C₂×C₃×D₄	—	2	8	no	—
189	C₂×C₃×D₄	—	2	4	no	—
190	C₂×C₃×D₄	—	2	8	no	—
191	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
192	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
193	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
194	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
195	C₂²×C₃×C₄	—	2	4	no	—
196	C₂²×C₃×C₄	—	2	4	no	—
197	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
198	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
199	C₃×SD₁₆	—	2	16	no	—
200	C₃×D₈	—	2	16	no	—
201	C₃×M₁₆	—	2	16	no	—
202	C₃×M₁₆	C₃×D₄	1	16	yes	complemented
203	C₂×C₃×C₈	—	2	8	no	—
204	C₂×C₃×C₈	—	2	16	no	—
205	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
206	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
207	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
208	C₃×C₄⋊C₄	—	2	4	no	—
209	C₃×C₄⋊C₄	—	2	8	no	—
210	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
211	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
212	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
213	C₃×C₂²⋊C₄	—	2	4	no	—
214	C₃×C₂²⋊C₄	—	2	8	no	—
215	C₃×C₂²⋊C₄	—	2	8	no	—
216	C₃×C₂²⋊C₄	—	2	8	no	—
217	C₃×C₂²⋊C₄	—	2	8	no	—
218	C₃×C₄²	—	2	4	no	—
219	C₂²×C₃²	—	2	1	no	—
220	C₂²×C₃²	—	2	1	no	—
221	C₂²×C₃²	—	2	2	no	—
222	C₂²×C₃²	—	2	2	no	—
223	C₂²×C₃²	—	2	2	no	—
224	C₂²×C₃²	—	4	1	no	—
225	C₂²×C₃²	—	4	2	no	—
226	C₂²×C₃²	—	4	1	no	—
227	C₂²×C₃²	—	4	2	no	—
228	C₂²×C₃²	—	4	2	no	—
229	C₂²×C₃²	—	4	1	no	—
230	C₂²×C₃²	—	8	4	no	—
231	C₂²×C₃²	#121	1	2	yes	—
232	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
233	C₃²×C₄	—	2	2	no	—
234	C₃²×C₄	—	4	1	no	—
235	C₃²×C₄	—	4	2	no	—
236	C₃²×C₄	—	4	1	no	—
237	C₃²×C₄	—	4	1	no	—
238	C₃²×C₄	#121	1	2	yes	—
239	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
240	C₃²×C₄	C₂×#41	1	1	yes	characteristic
241	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
242	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
243	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
244	AGL(1,ℤ/8)	—	2	4	no	—
245	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
246	C₂×D₈	C₂²×C₃²	1	2	yes	—
247	#131	—	2	4	no	—
248	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
249	C₂×M₁₆	C₂²×C₃²	1	2	yes	complemented
250	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
251	C₂²×C₈	C₂²×C₃²	1	2	yes	complemented
252	#127	—	2	1	no	—
253	#124	—	2	1	no	—
254	C₂²⋊Q₈	—	2	1	no	—
255	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
256	#121	—	2	1	no	—
257	#121	—	2	2	no	—
258	#121	C₂²×C₃²	1	2	yes	—
259	#121	C₂²×C₃²	1	2	yes	—
260	#121	C₂²×C₃²	1	2	yes	complemented
261	#120	—	2	2	no	—
262	#117	C₂²×C₃²	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
264	#107	C₂²×C₃²	1	2	yes	complemented
265	#106	C₂²×C₃²	1	2	yes	complemented
266	#103	C₂²×C₃²	1	1	yes	characteristic, complemented
267	#103	C₂²×C₃²	1	1	yes	characteristic, complemented
268	#102	C₂²×C₃²	1	2	yes	—
269	#102	C₂²×C₃²	1	2	yes	—
270	#102	C₂²×C₃²	1	1	yes	characteristic, complemented
271	#102	C₂²×C₃²	1	1	yes	characteristic, complemented
272	C₂³×C₃	—	2	4	no	—
273	C₂³×C₃	—	2	8	no	—
274	C₂³×C₃	—	4	8	no	—
275	C₂³×C₃	—	8	4	no	—
276	C₂³×C₃	—	8	4	no	—
277	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
278	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
279	C₃×Q₈	—	2	8	no	—
280	C₃×Q₈	—	2	4	no	—
281	C₃×Q₈	—	2	4	no	—
282	C₃×D₄	—	2	16	no	—
283	C₃×D₄	—	2	8	no	—
284	C₃×D₄	—	2	4	no	—
285	C₃×D₄	—	2	8	no	—
286	C₃×D₄	—	2	8	no	—
287	C₃×D₄	—	2	4	no	—
288	C₃×D₄	—	4	8	no	—
289	C₃×D₄	—	4	8	no	—
290	C₃×D₄	—	8	8	no	—
291	C₃×D₄	—	8	8	no	—
292	C₃×D₄	—	8	8	no	—
293	C₂×C₃×C₄	—	2	8	no	—
294	C₂×C₃×C₄	—	2	8	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	8	no	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	4	8	no	—
300	C₂×C₃×C₄	—	8	4	no	—
301	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
302	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
303	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
304	C₂×C₃×C₄	C₃×#41	1	8	yes	—
305	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
306	C₃×C₈	—	2	4	no	—
307	C₃×C₈	—	2	4	no	—
308	C₃×C₈	C₂×C₃×D₄	1	16	yes	—
309	C₂×C₃²	—	2	2	no	—
310	C₂×C₃²	—	4	2	no	—
311	C₂×C₃²	—	8	1	no	—
312	C₂×C₃²	—	8	2	no	—
313	C₂×C₃²	C₂×#121	1	1	yes	characteristic
314	C₂×C₃²	#576	1	1	yes	characteristic
315	C₂×C₃²	#577	1	1	yes	characteristic
316	C₂⁴	—	2	1	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	C₂×Q₈	C₃²×D₄	1	1	yes	characteristic
322	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	C₃²×D₄	1	2	yes	—
331	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
332	C₂×D₄	C₂³×C₃²	1	2	yes	—
333	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	C₂³×C₃²	1	2	yes	—
337	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
338	SD₁₆	—	2	4	no	—
339	D₈	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	M₁₆	C₃²×D₄	1	4	yes	complemented
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
345	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
346	C₂×C₈	C₂³×C₃²	1	2	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
350	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
351	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₄²	—	2	1	no	—
358	C₂²×C₃	—	2	4	no	—
359	C₂²×C₃	—	2	4	no	—
360	C₂²×C₃	—	2	8	no	—
361	C₂²×C₃	—	2	8	no	—
362	C₂²×C₃	—	2	8	no	—
363	C₂²×C₃	—	4	4	no	—
364	C₂²×C₃	—	4	8	no	—
365	C₂²×C₃	—	4	8	no	—
366	C₂²×C₃	—	4	4	no	—
367	C₂²×C₃	—	4	4	no	—
368	C₂²×C₃	—	4	8	no	—
369	C₂²×C₃	—	8	16	no	—
370	C₂²×C₃	C₃×#121	1	8	yes	—
371	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
372	C₃×C₄	—	2	8	no	—
373	C₃×C₄	—	4	8	no	—
374	C₃×C₄	—	4	4	no	—
375	C₃×C₄	—	4	4	no	—
376	C₃×C₄	—	4	4	no	—
377	C₃×C₄	C₃×#121	1	8	yes	—
378	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
379	C₃×C₄	C₂×C₃×#41	1	4	yes	—
380	C₃²	#3062	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	8	1	no	—
385	C₂³	—	8	1	no	—
386	C₂³	C₂×C₃²×D₄	1	2	yes	—
387	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	1	no	—
390	Q₈	—	2	1	no	—
391	D₄	—	2	4	no	—
392	D₄	—	2	1	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	1	no	—
396	D₄	—	2	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	2	no	—
401	D₄	—	8	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	1	no	—
410	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
411	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
412	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
413	C₂×C₄	C₃²×#41	1	2	yes	—
414	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	C₂×C₃²×D₄	1	4	yes	—
418	C₂×C₃	—	2	8	no	—
419	C₂×C₃	—	4	8	no	—
420	C₂×C₃	—	8	8	no	—
421	C₂×C₃	—	8	4	no	—
422	C₂×C₃	C₂×C₃×#121	1	4	yes	—
423	C₂×C₃	C₃×#576	1	4	yes	—
424	C₂×C₃	C₃×#577	1	4	yes	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	4	no	—
437	C₂²	C₃²×#121	1	2	yes	—
438	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	C₃²×#121	1	2	yes	—
445	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
446	C₄	C₂×C₃²×#41	1	1	yes	characteristic
447	C₃	C₃×#3062	1	4	yes	direct product factor
448	C₂	—	2	2	no	—
449	C₂	—	4	2	no	—
450	C₂	—	8	2	no	—
451	C₂	—	8	1	no	—
452	C₂	C₂×C₃²×#121	1	1	yes	characteristic
453	C₂	C₃²×#576	1	1	yes	characteristic
454	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 ◁ C₂×C₃²×#41 ◁ 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×#131	C₂	semidirect
3. C₃²×#537	C₂	semidirect
4. C₃²×#535	C₂	semidirect
5. C₃²×#469	C₂	semidirect
6. C₃²×#468	C₂	semidirect
7. C₃²×#466	C₂	semidirect
8. C₃²×#465	C₂	semidirect
9. C₃²×#428	C₂	semidirect
10. C₃²×#416	C₂	semidirect
11. C₂×C₃²×#102	C₂	semidirect
12. C₃×#3062	C₃	direct (N × H)
21. C₂×C₃²×M₁₆	C₂²	semidirect
23. C₂²×C₃²×C₈	C₂²	semidirect
27. C₃²×C₂²⋊Q₈	C₂²	semidirect
32. C₃²×#121	C₂²	semidirect
36. C₃²×#107	C₂²	semidirect
37. C₃²×#106	C₂²	semidirect
38. C₃²×#103	C₂²	semidirect
39. C₃²×#103	C₂²	semidirect
42. C₃²×#102	C₂²	semidirect
43. C₃²×#102	C₂²	semidirect
44. C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	semidirect
45. C₂×C₃×#131	C₂×C₃	semidirect
46. C₃×#537	C₂×C₃	semidirect
47. C₃×#535	C₂×C₃	semidirect
48. C₃×#469	C₂×C₃	semidirect
49. C₃×#468	C₂×C₃	semidirect
50. C₃×#466	C₂×C₃	semidirect
51. C₃×#465	C₂×C₃	semidirect
52. C₃×#428	C₂×C₃	semidirect
53. C₃×#416	C₂×C₃	semidirect
54. C₂×C₃×#102	C₂×C₃	semidirect
80. C₃²×M₁₆	D₄	semidirect
97. #3062	C₃²	direct (N × H)
106. C₂×C₃×M₁₆	C₂²×C₃	semidirect
108. C₂²×C₃×C₈	C₂²×C₃	semidirect
112. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
117. C₃×#121	C₂²×C₃	semidirect
121. C₃×#107	C₂²×C₃	semidirect
122. C₃×#106	C₂²×C₃	semidirect
123. C₃×#103	C₂²×C₃	semidirect
124. C₃×#103	C₂²×C₃	semidirect
127. C₃×#102	C₂²×C₃	semidirect
128. C₃×#102	C₂²×C₃	semidirect
166. C₂×AGL(1,ℤ/8)	C₂×C₃²	semidirect
167. C₂×#131	C₂×C₃²	semidirect
168. #537	C₂×C₃²	semidirect
169. #535	C₂×C₃²	semidirect
170. #469	C₂×C₃²	semidirect
171. #468	C₂×C₃²	semidirect
172. #466	C₂×C₃²	semidirect
173. #465	C₂×C₃²	semidirect
174. #428	C₂×C₃²	semidirect
175. #416	C₂×C₃²	semidirect
176. C₂×#102	C₂×C₃²	semidirect
202. C₃×M₁₆	C₃×D₄	semidirect
249. C₂×M₁₆	C₂²×C₃²	semidirect
251. C₂²×C₈	C₂²×C₃²	semidirect
255. C₂²⋊Q₈	C₂²×C₃²	semidirect
260. #121	C₂²×C₃²	semidirect
264. #107	C₂²×C₃²	semidirect
265. #106	C₂²×C₃²	semidirect
266. #103	C₂²×C₃²	semidirect
267. #103	C₂²×C₃²	semidirect
270. #102	C₂²×C₃²	semidirect
271. #102	C₂²×C₃²	semidirect
341. M₁₆	C₃²×D₄	semidirect
380. C₃²	#3062	direct (N × H)
447. C₃	C₃×#3062	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×#131	2
C₃²×#537	2
C₃²×#535	2
C₃²×#469	2
C₃²×#468	2
C₃²×#466	2
C₃²×#465	2
C₃²×#428	2
C₃²×#416	2
C₂×C₃²×#102	2
C₃×#3062	3

Subgroups — C32×#3062 #11770111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3062 #11770111