Subgroups — C₂×C₃²×#471 #11770113

Order 1152.

1404 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃²×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#471	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃²×#101	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃²×#100	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#471	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
13	C₃²×#137	—	2	2	no	—
14	C₃²×#137	C₂²	1	4	yes	complemented
15	C₃²×AGL(1,ℤ/8)	—	2	2	no	—
16	C₃²×AGL(1,ℤ/8)	C₂²	1	4	yes	—
17	C₂×C₃²×Q₁₆	—	2	1	no	—
18	C₂×C₃²×SD₁₆	—	2	1	no	—
19	C₂×C₃²×SD₁₆	—	2	1	no	—
20	C₂×C₃²×SD₁₆	—	2	1	no	—
21	C₂×C₃²×SD₁₆	—	2	1	no	—
22	C₂×C₃²×SD₁₆	—	2	2	no	—
23	C₂×C₃²×SD₁₆	C₂²	1	4	yes	complemented
24	C₂×C₃²×D₈	—	2	1	no	—
25	C₃²×#131	—	2	2	no	—
26	C₃²×#131	C₂²	1	4	yes	complemented
27	C₂×C₃²×M₁₆	—	2	1	no	—
28	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
31	C₂²×C₃²×C₈	—	2	1	no	—
32	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
33	C₃²×#108	C₂²	1	4	yes	complemented
34	C₃²×#101	C₂²	1	4	yes	complemented
35	C₃²×#100	C₂²	1	4	yes	complemented
36	C₂×C₃×#137	C₂×C₃	1	4	yes	complemented
37	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	4	yes	—
38	C₂²×C₃×SD₁₆	C₂×C₃	1	4	yes	complemented
39	C₂×C₃×#131	C₂×C₃	1	4	yes	complemented
40	C₃×#471	C₂×C₃	1	32	yes	direct product factor
41	C₂×C₃×#108	C₂×C₃	1	4	yes	complemented
42	C₂×C₃×#101	C₂×C₃	1	4	yes	complemented
43	C₂×C₃×#100	C₂×C₃	1	4	yes	complemented
44	C₂⁴×C₃²	—	2	1	no	—
45	C₃²×#41	—	2	1	no	—
46	C₃²×#41	—	2	1	no	—
47	C₃²×#41	D₄	1	2	yes	—
48	C₃²×#41	C₂³	1	2	yes	—
49	C₂×C₃²×Q₈	—	2	1	no	—
50	C₂×C₃²×Q₈	—	2	1	no	—
51	C₂×C₃²×Q₈	—	2	1	no	—
52	C₂×C₃²×Q₈	—	2	1	no	—
53	C₂×C₃²×Q₈	—	2	1	no	—
54	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
55	C₂×C₃²×Q₈	C₂³	1	2	yes	—
56	C₂×C₃²×D₄	—	2	1	no	—
57	C₂×C₃²×D₄	—	2	1	no	—
58	C₂×C₃²×D₄	—	2	1	no	—
59	C₂×C₃²×D₄	—	2	1	no	—
60	C₂×C₃²×D₄	—	2	1	no	—
61	C₂×C₃²×D₄	—	2	1	no	—
62	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
63	C₂×C₃²×D₄	C₂³	1	2	yes	—
64	C₂²×C₃²×C₄	—	2	1	no	—
65	C₂²×C₃²×C₄	—	2	1	no	—
66	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
67	C₃²×Q₁₆	—	2	4	no	—
68	C₃²×SD₁₆	—	2	4	no	—
69	C₃²×SD₁₆	—	2	4	no	—
70	C₃²×SD₁₆	—	2	4	no	—
71	C₃²×SD₁₆	—	2	4	no	—
72	C₃²×D₈	—	2	4	no	—
73	C₃²×M₁₆	—	2	1	no	—
74	C₃²×M₁₆	—	2	1	no	—
75	C₃²×M₁₆	—	2	1	no	—
76	C₃²×M₁₆	—	2	4	no	—
77	C₃²×M₁₆	C₂³	1	2	yes	—
78	C₃²×M₁₆	C₂³	1	2	yes	—
79	C₃²×M₁₆	C₂³	1	2	yes	—
80	C₂×C₃²×C₈	—	2	1	no	—
81	C₂×C₃²×C₈	—	2	1	no	—
82	C₂×C₃²×C₈	—	2	1	no	—
83	C₂×C₃²×C₈	—	2	4	no	—
84	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
85	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
86	C₂×C₃²×C₈	D₄	1	2	yes	—
87	C₂×C₃²×C₈	C₂³	1	2	yes	—
88	C₂×#471	C₃²	1	1	yes	characteristic, direct product factor, Sylow
89	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
90	C₂²×C₃×Q₈	C₂²×C₃	1	4	yes	—
91	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
92	C₃×#137	—	2	8	no	—
93	C₃×#137	C₂²×C₃	1	16	yes	complemented
94	C₃×AGL(1,ℤ/8)	—	2	8	no	—
95	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	16	yes	—
96	C₂×C₃×Q₁₆	—	2	4	no	—
97	C₂×C₃×SD₁₆	—	2	4	no	—
98	C₂×C₃×SD₁₆	—	2	4	no	—
99	C₂×C₃×SD₁₆	—	2	4	no	—
100	C₂×C₃×SD₁₆	—	2	4	no	—
101	C₂×C₃×SD₁₆	—	2	8	no	—
102	C₂×C₃×SD₁₆	C₂²×C₃	1	16	yes	complemented
103	C₂×C₃×D₈	—	2	4	no	—
104	C₃×#131	—	2	8	no	—
105	C₃×#131	C₂²×C₃	1	16	yes	complemented
106	C₂×C₃×M₁₆	—	2	4	no	—
107	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
108	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
109	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
110	C₂²×C₃×C₈	—	2	4	no	—
111	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
112	C₃×#108	C₂²×C₃	1	16	yes	complemented
113	C₃×#101	C₂²×C₃	1	16	yes	complemented
114	C₃×#100	C₂²×C₃	1	16	yes	complemented
115	C₂³×C₃²	—	2	1	no	—
116	C₂³×C₃²	—	2	2	no	—
117	C₂³×C₃²	—	4	1	no	—
118	C₂³×C₃²	—	4	1	no	—
119	C₂³×C₃²	—	8	2	no	—
120	C₂³×C₃²	#41	1	1	yes	characteristic
121	C₃²×Q₈	—	2	1	no	—
122	C₃²×Q₈	—	2	2	no	—
123	C₃²×Q₈	—	2	2	no	—
124	C₃²×Q₈	—	4	1	no	—
125	C₃²×Q₈	—	4	1	no	—
126	C₃²×Q₈	C₂×D₄	1	2	yes	—
127	C₃²×D₄	—	2	2	no	—
128	C₃²×D₄	—	2	2	no	—
129	C₃²×D₄	—	2	1	no	—
130	C₃²×D₄	—	2	2	no	—
131	C₃²×D₄	—	2	2	no	—
132	C₃²×D₄	—	4	1	no	—
133	C₃²×D₄	—	4	1	no	—
134	C₃²×D₄	C₂×D₄	1	2	yes	—
135	C₂×C₃²×C₄	—	2	1	no	—
136	C₂×C₃²×C₄	—	2	2	no	—
137	C₂×C₃²×C₄	—	2	2	no	—
138	C₂×C₃²×C₄	—	2	2	no	—
139	C₂×C₃²×C₄	—	4	1	no	—
140	C₂×C₃²×C₄	—	4	1	no	—
141	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃²×C₄	#41	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
147	C₃²×C₈	—	2	2	no	—
148	C₃²×C₈	—	2	2	no	—
149	C₃²×C₈	—	2	2	no	—
150	C₃²×C₈	C₂×D₄	1	2	yes	—
151	C₃²×C₈	C₂×D₄	1	2	yes	—
152	C₂×#137	C₂×C₃²	1	1	yes	characteristic, complemented
153	C₂×AGL(1,ℤ/8)	C₂×C₃²	1	1	yes	characteristic
154	C₂²×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
155	C₂×#131	C₂×C₃²	1	1	yes	characteristic, complemented
156	#471	C₂×C₃²	1	8	yes	direct product factor
157	C₂×#108	C₂×C₃²	1	1	yes	characteristic, complemented
158	C₂×#101	C₂×C₃²	1	1	yes	characteristic, complemented
159	C₂×#100	C₂×C₃²	1	1	yes	characteristic, complemented
160	C₂⁴×C₃	—	2	4	no	—
161	C₃×#41	—	2	4	no	—
162	C₃×#41	—	2	4	no	—
163	C₃×#41	C₃×D₄	1	8	yes	—
164	C₃×#41	C₂³×C₃	1	8	yes	—
165	C₂×C₃×Q₈	—	2	4	no	—
166	C₂×C₃×Q₈	—	2	4	no	—
167	C₂×C₃×Q₈	—	2	4	no	—
168	C₂×C₃×Q₈	—	2	4	no	—
169	C₂×C₃×Q₈	—	2	4	no	—
170	C₂×C₃×Q₈	C₃×D₄	1	4	yes	—
171	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
172	C₂×C₃×D₄	—	2	4	no	—
173	C₂×C₃×D₄	—	2	4	no	—
174	C₂×C₃×D₄	—	2	4	no	—
175	C₂×C₃×D₄	—	2	4	no	—
176	C₂×C₃×D₄	—	2	4	no	—
177	C₂×C₃×D₄	—	2	4	no	—
178	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
179	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
180	C₂²×C₃×C₄	—	2	4	no	—
181	C₂²×C₃×C₄	—	2	4	no	—
182	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
183	C₃×Q₁₆	—	2	16	no	—
184	C₃×SD₁₆	—	2	16	no	—
185	C₃×SD₁₆	—	2	16	no	—
186	C₃×SD₁₆	—	2	16	no	—
187	C₃×SD₁₆	—	2	16	no	—
188	C₃×D₈	—	2	16	no	—
189	C₃×M₁₆	—	2	4	no	—
190	C₃×M₁₆	—	2	4	no	—
191	C₃×M₁₆	—	2	4	no	—
192	C₃×M₁₆	—	2	16	no	—
193	C₃×M₁₆	C₂³×C₃	1	8	yes	—
194	C₃×M₁₆	C₂³×C₃	1	8	yes	—
195	C₃×M₁₆	C₂³×C₃	1	8	yes	—
196	C₂×C₃×C₈	—	2	4	no	—
197	C₂×C₃×C₈	—	2	4	no	—
198	C₂×C₃×C₈	—	2	4	no	—
199	C₂×C₃×C₈	—	2	16	no	—
200	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
201	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
202	C₂×C₃×C₈	C₃×D₄	1	8	yes	—
203	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
204	C₂²×C₃²	—	2	2	no	—
205	C₂²×C₃²	—	2	2	no	—
206	C₂²×C₃²	—	4	2	no	—
207	C₂²×C₃²	—	4	2	no	—
208	C₂²×C₃²	—	8	2	no	—
209	C₂²×C₃²	—	8	2	no	—
210	C₂²×C₃²	—	8	2	no	—
211	C₂²×C₃²	#121	1	1	yes	characteristic
212	C₂²×C₃²	#121	1	1	yes	characteristic
213	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
214	C₃²×C₄	—	2	2	no	—
215	C₃²×C₄	—	4	2	no	—
216	C₃²×C₄	#121	1	1	yes	characteristic
217	C₃²×C₄	#121	1	1	yes	characteristic
218	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
219	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
220	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
221	C₂²×Q₈	C₂²×C₃²	1	1	yes	characteristic
222	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
223	#137	—	2	2	no	—
224	#137	C₂²×C₃²	1	4	yes	complemented
225	AGL(1,ℤ/8)	—	2	2	no	—
226	AGL(1,ℤ/8)	C₂²×C₃²	1	4	yes	—
227	C₂×Q₁₆	—	2	1	no	—
228	C₂×SD₁₆	—	2	1	no	—
229	C₂×SD₁₆	—	2	1	no	—
230	C₂×SD₁₆	—	2	1	no	—
231	C₂×SD₁₆	—	2	1	no	—
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×SD₁₆	C₂²×C₃²	1	4	yes	complemented
234	C₂×D₈	—	2	1	no	—
235	#131	—	2	2	no	—
236	#131	C₂²×C₃²	1	4	yes	complemented
237	C₂×M₁₆	—	2	1	no	—
238	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
239	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
240	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
243	#108	C₂²×C₃²	1	4	yes	complemented
244	#101	C₂²×C₃²	1	4	yes	complemented
245	#100	C₂²×C₃²	1	4	yes	complemented
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	—	2	8	no	—
248	C₂³×C₃	—	4	4	no	—
249	C₂³×C₃	—	4	4	no	—
250	C₂³×C₃	—	8	8	no	—
251	C₂³×C₃	C₃×#41	1	4	yes	—
252	C₃×Q₈	—	2	4	no	—
253	C₃×Q₈	—	2	8	no	—
254	C₃×Q₈	—	2	8	no	—
255	C₃×Q₈	—	4	4	no	—
256	C₃×Q₈	—	4	4	no	—
257	C₃×Q₈	C₂×C₃×D₄	1	8	yes	—
258	C₃×D₄	—	2	8	no	—
259	C₃×D₄	—	2	8	no	—
260	C₃×D₄	—	2	4	no	—
261	C₃×D₄	—	2	8	no	—
262	C₃×D₄	—	2	8	no	—
263	C₃×D₄	—	4	4	no	—
264	C₃×D₄	—	4	4	no	—
265	C₃×D₄	C₂×C₃×D₄	1	8	yes	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	8	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	2	8	no	—
270	C₂×C₃×C₄	—	4	4	no	—
271	C₂×C₃×C₄	—	4	4	no	—
272	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
273	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
274	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
275	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
276	C₂×C₃×C₄	C₃×#41	1	4	yes	—
277	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
278	C₃×C₈	—	2	8	no	—
279	C₃×C₈	—	2	8	no	—
280	C₃×C₈	—	2	8	no	—
281	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
282	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
283	C₂×C₃²	—	2	1	no	—
284	C₂×C₃²	—	2	1	no	—
285	C₂×C₃²	—	4	2	no	—
286	C₂×C₃²	—	8	2	no	—
287	C₂×C₃²	#471	1	2	yes	direct product factor
288	C₂×C₃²	C₂×#121	1	1	yes	characteristic
289	C₂⁴	—	2	1	no	—
290	#41	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	C₃²×D₄	1	2	yes	—
293	#41	C₂³×C₃²	1	2	yes	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	C₃²×D₄	1	1	yes	characteristic
300	C₂×Q₈	C₂³×C₃²	1	2	yes	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
308	C₂×D₄	C₂³×C₃²	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
312	Q₁₆	—	2	4	no	—
313	SD₁₆	—	2	4	no	—
314	SD₁₆	—	2	4	no	—
315	SD₁₆	—	2	4	no	—
316	SD₁₆	—	2	4	no	—
317	D₈	—	2	4	no	—
318	M₁₆	—	2	1	no	—
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	1	no	—
321	M₁₆	—	2	4	no	—
322	M₁₆	C₂³×C₃²	1	2	yes	—
323	M₁₆	C₂³×C₃²	1	2	yes	—
324	M₁₆	C₂³×C₃²	1	2	yes	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
330	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
331	C₂×C₈	C₃²×D₄	1	2	yes	—
332	C₂×C₈	C₂³×C₃²	1	2	yes	—
333	C₂²×C₃	—	2	8	no	—
334	C₂²×C₃	—	2	8	no	—
335	C₂²×C₃	—	4	8	no	—
336	C₂²×C₃	—	4	8	no	—
337	C₂²×C₃	—	8	8	no	—
338	C₂²×C₃	—	8	8	no	—
339	C₂²×C₃	—	8	8	no	—
340	C₂²×C₃	C₃×#121	1	4	yes	—
341	C₂²×C₃	C₃×#121	1	4	yes	—
342	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
343	C₃×C₄	—	2	8	no	—
344	C₃×C₄	—	4	8	no	—
345	C₃×C₄	C₃×#121	1	4	yes	—
346	C₃×C₄	C₃×#121	1	4	yes	—
347	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
348	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
349	C₃²	C₂×#471	1	1	yes	characteristic, direct product factor, Sylow
350	C₂³	—	2	1	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	8	2	no	—
355	C₂³	C₃²×#41	1	1	yes	characteristic
356	Q₈	—	2	1	no	—
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	4	1	no	—
360	Q₈	—	4	1	no	—
361	Q₈	C₂×C₃²×D₄	1	2	yes	—
362	D₄	—	2	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	C₂×C₃²×D₄	1	2	yes	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
377	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
378	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
379	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
380	C₂×C₄	C₃²×#41	1	1	yes	characteristic
381	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	2	2	no	—
385	C₈	C₂×C₃²×D₄	1	2	yes	—
386	C₈	C₂×C₃²×D₄	1	2	yes	—
387	C₂×C₃	—	2	4	no	—
388	C₂×C₃	—	2	4	no	—
389	C₂×C₃	—	4	8	no	—
390	C₂×C₃	—	8	8	no	—
391	C₂×C₃	C₃×#471	1	8	yes	direct product factor
392	C₂×C₃	C₂×C₃×#121	1	4	yes	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	C₃²×#121	1	1	yes	characteristic
401	C₂²	C₃²×#121	1	1	yes	characteristic
402	C₂²	C₂×C₃²×#41	1	1	yes	characteristic
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	C₃²×#121	1	1	yes	characteristic
406	C₄	C₃²×#121	1	1	yes	characteristic
407	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
408	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
409	C₃	C₂×C₃×#471	1	4	yes	direct product factor
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	4	2	no	—
413	C₂	—	8	2	no	—
414	C₂	C₃²×#471	1	2	yes	direct product factor
415	C₂	C₂×C₃²×#121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
prime radical	C₂×C₃²×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#137	C₂	semidirect
3. C₂²×C₃²×SD₁₆	C₂	semidirect
4. C₂×C₃²×#131	C₂	semidirect
5. C₃²×#471	C₂	direct (N × H)
6. C₂×C₃²×#108	C₂	semidirect
7. C₂×C₃²×#101	C₂	semidirect
8. C₂×C₃²×#100	C₂	semidirect
9. C₂×C₃×#471	C₃	direct (N × H)
14. C₃²×#137	C₂²	semidirect
23. C₂×C₃²×SD₁₆	C₂²	semidirect
26. C₃²×#131	C₂²	semidirect
33. C₃²×#108	C₂²	semidirect
34. C₃²×#101	C₂²	semidirect
35. C₃²×#100	C₂²	semidirect
36. C₂×C₃×#137	C₂×C₃	semidirect
38. C₂²×C₃×SD₁₆	C₂×C₃	semidirect
39. C₂×C₃×#131	C₂×C₃	semidirect
40. C₃×#471	C₂×C₃	direct (N × H)
41. C₂×C₃×#108	C₂×C₃	semidirect
42. C₂×C₃×#101	C₂×C₃	semidirect
43. C₂×C₃×#100	C₂×C₃	semidirect
88. C₂×#471	C₃²	direct (N × H)
93. C₃×#137	C₂²×C₃	semidirect
102. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
105. C₃×#131	C₂²×C₃	semidirect
112. C₃×#108	C₂²×C₃	semidirect
113. C₃×#101	C₂²×C₃	semidirect
114. C₃×#100	C₂²×C₃	semidirect
152. C₂×#137	C₂×C₃²	semidirect
154. C₂²×SD₁₆	C₂×C₃²	semidirect
155. C₂×#131	C₂×C₃²	semidirect
156. #471	C₂×C₃²	direct (N × H)
157. C₂×#108	C₂×C₃²	semidirect
158. C₂×#101	C₂×C₃²	semidirect
159. C₂×#100	C₂×C₃²	semidirect
224. #137	C₂²×C₃²	semidirect
233. C₂×SD₁₆	C₂²×C₃²	semidirect
236. #131	C₂²×C₃²	semidirect
243. #108	C₂²×C₃²	semidirect
244. #101	C₂²×C₃²	semidirect
245. #100	C₂²×C₃²	semidirect
287. C₂×C₃²	#471	direct (N × H)
349. C₃²	C₂×#471	direct (N × H)
391. C₂×C₃	C₃×#471	direct (N × H)
409. C₃	C₂×C₃×#471	direct (N × H)
414. C₂	C₃²×#471	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×#137	2
C₂×C₃²×AGL(1,ℤ/8)	2
C₂²×C₃²×SD₁₆	2
C₂×C₃²×#131	2
C₃²×#471	2
C₂×C₃²×#108	2
C₂×C₃²×#101	2
C₂×C₃²×#100	2
C₂×C₃×#471	3

Subgroups — C2×C32×#471 #11770113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#471 #11770113