Subgroups — C₂×C₃×#3208 #10679382

Order 768.

2822 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₃×#3208	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#492	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#486	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#460	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#450	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#3208	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₃×D₄	—	2	1	no	—
11	C₂³×C₃×D₄	—	2	1	no	—
12	C₂³×C₃×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×SD₁₆	C₂²	1	8	yes	complemented
14	C₃×#533	—	2	4	no	—
15	C₃×#533	C₂²	1	8	yes	complemented
16	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×#127	—	2	1	no	—
19	C₂×C₃×#127	—	2	1	no	—
20	C₂×C₃×#127	—	2	4	no	—
21	C₂×C₃×#127	C₂²	1	2	yes	—
22	C₂×C₃×#127	C₂²	1	8	yes	—
23	C₂×C₃×#127	C₂²	1	2	yes	—
24	C₂×C₃×#125	—	2	1	no	—
25	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃×C₄×Q₈	—	2	1	no	—
28	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
29	C₂×C₃×#117	—	2	1	no	—
30	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
31	C₃×#492	C₂²	1	16	yes	complemented
32	C₃×#486	C₂²	1	16	yes	complemented
33	C₃×#460	C₂²	1	32	yes	complemented
34	C₃×#450	C₂²	1	32	yes	complemented
35	C₃×#431	C₂²	1	8	yes	complemented
36	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	complemented
37	C₂×C₃×#102	C₂²	1	8	yes	complemented
38	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₂×C₃×C₄×C₈	C₂²	1	2	yes	complemented
40	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂²×#127	C₂×C₃	1	1	yes	characteristic
42	#3208	C₂×C₃	1	16	yes	direct product factor
43	C₂×#492	C₂×C₃	1	2	yes	complemented
44	C₂×#486	C₂×C₃	1	2	yes	complemented
45	C₂×#460	C₂×C₃	1	4	yes	complemented
46	C₂×#450	C₂×C₃	1	4	yes	complemented
47	C₂×#431	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂⁵×C₃	—	2	2	no	—
49	C₂²×C₃×Q₈	—	2	1	no	—
50	C₂²×C₃×Q₈	C₂³	1	2	yes	—
51	C₂²×C₃×D₄	—	2	8	no	—
52	C₂²×C₃×D₄	—	2	2	no	—
53	C₂²×C₃×D₄	—	2	2	no	—
54	C₂²×C₃×D₄	—	2	2	no	—
55	C₂²×C₃×D₄	—	2	8	no	—
56	C₂²×C₃×D₄	—	2	2	no	—
57	C₂²×C₃×D₄	—	2	4	no	—
58	C₂²×C₃×D₄	—	2	2	no	—
59	C₂²×C₃×D₄	—	4	8	no	—
60	C₂²×C₃×D₄	—	4	8	no	—
61	C₂²×C₃×D₄	—	4	8	no	—
62	C₂²×C₃×D₄	C₂³	1	4	yes	—
63	C₂²×C₃×D₄	C₂³	1	8	yes	—
64	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
65	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
66	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃×SD₁₆	—	4	16	no	—
68	C₂×C₃×SD₁₆	C₂³	1	32	yes	complemented
69	C₂²×C₃×C₈	C₂³	1	4	yes	—
70	C₃×C₄⋊Q₈	—	2	2	no	—
71	C₃×C₄⋊Q₈	—	2	2	no	—
72	C₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
73	C₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
74	C₃×#127	—	2	8	no	—
75	C₃×#127	—	2	4	no	—
76	C₃×#127	—	2	8	no	—
77	C₃×#127	—	2	4	no	—
78	C₃×#127	C₂³	1	8	yes	—
79	C₃×#127	C₂³	1	8	yes	—
80	C₃×#125	—	2	8	no	—
81	C₃×C₂²⋊Q₈	—	2	8	no	—
82	C₃×C₂²⋊Q₈	—	2	4	no	—
83	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
84	C₃×C₄×Q₈	—	2	8	no	—
85	C₃×C₄×Q₈	—	2	4	no	—
86	C₃×C₄×Q₈	C₂³	1	8	yes	complemented
87	C₃×#117	—	2	8	no	—
88	C₂×C₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₃×C₄⋊C₄	—	2	2	no	—
93	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₃×C₄²	—	2	2	no	—
96	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
97	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
98	C₂×C₃×C₄²	D₄	1	4	yes	—
99	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄²	C₂³	1	4	yes	—
102	C₃×C₄⋊C₈	C₂³	1	8	yes	complemented
103	C₃×#102	C₂³	1	32	yes	complemented
104	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
105	C₃×C₄×C₈	C₂³	1	8	yes	complemented
106	C₂³×D₄	—	2	1	no	—
107	C₂³×D₄	—	2	1	no	—
108	C₂³×D₄	C₂²×C₃	1	2	yes	—
109	C₂²×SD₁₆	C₂²×C₃	1	8	yes	complemented
110	#533	—	2	4	no	—
111	#533	C₂²×C₃	1	8	yes	complemented
112	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂×#127	—	2	1	no	—
115	C₂×#127	—	2	1	no	—
116	C₂×#127	—	2	4	no	—
117	C₂×#127	C₂²×C₃	1	2	yes	—
118	C₂×#127	C₂²×C₃	1	8	yes	—
119	C₂×#127	C₂²×C₃	1	2	yes	—
120	C₂×#125	—	2	1	no	—
121	C₂×C₂²⋊Q₈	—	2	1	no	—
122	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
123	C₂×C₄×Q₈	—	2	1	no	—
124	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
125	C₂×#117	—	2	1	no	—
126	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
127	#492	C₂²×C₃	1	16	yes	complemented
128	#486	C₂²×C₃	1	16	yes	complemented
129	#460	C₂²×C₃	1	32	yes	complemented
130	#450	C₂²×C₃	1	32	yes	complemented
131	#431	C₂²×C₃	1	8	yes	complemented
132	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
133	C₂×#102	C₂²×C₃	1	8	yes	complemented
134	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
135	C₂×C₄×C₈	C₂²×C₃	1	2	yes	complemented
136	C₂⁴×C₃	—	2	8	no	—
137	C₂⁴×C₃	—	2	4	no	—
138	C₂⁴×C₃	—	4	8	no	—
139	C₂⁴×C₃	—	4	8	no	—
140	C₂⁴×C₃	—	4	8	no	—
141	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×Q₈	—	2	2	no	—
143	C₂×C₃×Q₈	—	2	4	no	—
144	C₂×C₃×Q₈	—	2	8	no	—
145	C₂×C₃×Q₈	—	4	4	no	—
146	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
147	C₂×C₃×D₄	—	2	8	no	—
148	C₂×C₃×D₄	—	2	4	no	—
149	C₂×C₃×D₄	—	2	8	no	—
150	C₂×C₃×D₄	—	2	8	no	—
151	C₂×C₃×D₄	—	2	8	no	—
152	C₂×C₃×D₄	—	2	8	no	—
153	C₂×C₃×D₄	—	2	16	no	—
154	C₂×C₃×D₄	—	4	16	no	—
155	C₂×C₃×D₄	—	4	8	no	—
156	C₂×C₃×D₄	—	4	8	no	—
157	C₂×C₃×D₄	—	4	16	no	—
158	C₂×C₃×D₄	—	4	32	no	—
159	C₂×C₃×D₄	—	4	8	no	—
160	C₂×C₃×D₄	—	4	8	no	—
161	C₂×C₃×D₄	—	4	32	no	—
162	C₂×C₃×D₄	—	4	8	no	—
163	C₂×C₃×D₄	C₂⁴	1	8	yes	—
164	C₂²×C₃×C₄	—	2	4	no	—
165	C₂²×C₃×C₄	—	2	4	no	—
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	—	2	2	no	—
168	C₂²×C₃×C₄	SD₁₆	1	8	yes	complemented
169	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
170	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
171	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
176	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
178	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
179	C₃×SD₁₆	—	4	32	no	—
180	C₂×C₃×C₈	—	2	8	no	—
181	C₂×C₃×C₈	C₂⁴	1	8	yes	—
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	2	4	no	—
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	—	2	8	no	—
186	C₃×C₄⋊C₄	—	2	8	no	—
187	C₃×C₄⋊C₄	—	2	2	no	—
188	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
189	C₃×C₂²⋊C₄	—	2	8	no	—
190	C₃×C₄²	—	2	8	no	—
191	C₃×C₄²	C₂×D₄	1	4	yes	—
192	C₃×C₄²	C₂×D₄	1	2	yes	—
193	C₃×C₄²	C₂×D₄	1	4	yes	—
194	C₃×C₄²	C₂×D₄	1	2	yes	—
195	C₃×C₄²	C₂⁴	1	2	yes	—
196	C₃×C₄²	C₂⁴	1	2	yes	—
197	C₂⁵	—	2	2	no	—
198	C₂²×Q₈	—	2	1	no	—
199	C₂²×Q₈	C₂³×C₃	1	2	yes	—
200	C₂²×D₄	—	2	2	no	—
201	C₂²×D₄	—	2	4	no	—
202	C₂²×D₄	—	2	2	no	—
203	C₂²×D₄	—	2	8	no	—
204	C₂²×D₄	—	2	2	no	—
205	C₂²×D₄	—	2	2	no	—
206	C₂²×D₄	—	2	8	no	—
207	C₂²×D₄	—	2	2	no	—
208	C₂²×D₄	—	4	8	no	—
209	C₂²×D₄	—	4	8	no	—
210	C₂²×D₄	—	4	8	no	—
211	C₂²×D₄	C₂³×C₃	1	4	yes	—
212	C₂²×D₄	C₂³×C₃	1	8	yes	—
213	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
214	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
216	C₂×SD₁₆	—	4	16	no	—
217	C₂×SD₁₆	C₂³×C₃	1	32	yes	complemented
218	C₂²×C₈	C₂³×C₃	1	4	yes	—
219	C₄⋊Q₈	—	2	2	no	—
220	C₄⋊Q₈	—	2	2	no	—
221	C₄⋊Q₈	C₂³×C₃	1	4	yes	complemented
222	C₄⋊Q₈	C₂³×C₃	1	4	yes	complemented
223	#127	—	2	8	no	—
224	#127	—	2	4	no	—
225	#127	—	2	8	no	—
226	#127	—	2	4	no	—
227	#127	C₂³×C₃	1	8	yes	—
228	#127	C₂³×C₃	1	8	yes	—
229	#125	—	2	8	no	—
230	C₂²⋊Q₈	—	2	8	no	—
231	C₂²⋊Q₈	—	2	4	no	—
232	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
233	C₄×Q₈	—	2	8	no	—
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	C₂³×C₃	1	8	yes	complemented
236	#117	—	2	8	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
246	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
247	C₂×C₄²	C₃×D₄	1	4	yes	—
248	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₃	1	4	yes	—
251	C₄⋊C₈	C₂³×C₃	1	8	yes	complemented
252	#102	C₂³×C₃	1	32	yes	complemented
253	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
254	C₄×C₈	C₂³×C₃	1	8	yes	complemented
255	C₂³×C₃	—	2	2	no	—
256	C₂³×C₃	—	2	2	no	—
257	C₂³×C₃	—	2	8	no	—
258	C₂³×C₃	—	4	16	no	—
259	C₂³×C₃	—	4	16	no	—
260	C₂³×C₃	—	4	8	no	—
261	C₂³×C₃	—	4	16	no	—
262	C₂³×C₃	—	4	8	no	—
263	C₂³×C₃	—	4	8	no	—
264	C₂³×C₃	—	8	32	no	—
265	C₂³×C₃	C₂×SD₁₆	1	4	yes	—
266	C₂³×C₃	C₂²×D₄	1	2	yes	—
267	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
268	C₃×Q₈	—	2	8	no	—
269	C₃×Q₈	—	4	4	no	—
270	C₃×Q₈	—	4	8	no	—
271	C₃×D₄	—	2	16	no	—
272	C₃×D₄	—	4	16	no	—
273	C₃×D₄	—	4	16	no	—
274	C₃×D₄	—	4	8	no	—
275	C₃×D₄	—	4	16	no	—
276	C₃×D₄	—	4	16	no	—
277	C₃×D₄	—	4	16	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	8	no	—
282	C₂×C₃×C₄	—	2	4	no	—
283	C₂×C₃×C₄	—	2	4	no	—
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	4	4	no	—
286	C₂×C₃×C₄	—	4	4	no	—
287	C₂×C₃×C₄	C₂×SD₁₆	1	4	yes	—
288	C₂×C₃×C₄	C₂×SD₁₆	1	4	yes	—
289	C₂×C₃×C₄	C₂×SD₁₆	1	16	yes	complemented
290	C₂×C₃×C₄	AGL(1,ℤ/8)	1	4	yes	—
291	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
292	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
293	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
295	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
297	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
298	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
299	C₃×C₈	—	2	8	no	—
300	C₂⁴	—	2	8	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	4	8	no	—
303	C₂⁴	—	4	8	no	—
304	C₂⁴	—	4	8	no	—
305	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	8	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	—	2	16	no	—
318	C₂×D₄	—	4	16	no	—
319	C₂×D₄	—	4	8	no	—
320	C₂×D₄	—	4	8	no	—
321	C₂×D₄	—	4	32	no	—
322	C₂×D₄	—	4	16	no	—
323	C₂×D₄	—	4	8	no	—
324	C₂×D₄	—	4	8	no	—
325	C₂×D₄	—	4	32	no	—
326	C₂×D₄	—	4	8	no	—
327	C₂×D₄	C₂⁴×C₃	1	8	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	C₃×SD₁₆	1	8	yes	complemented
333	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
335	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
337	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
340	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
343	SD₁₆	—	4	32	no	—
344	C₂×C₈	—	2	8	no	—
345	C₂×C₈	C₂⁴×C₃	1	8	yes	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₄²	—	2	8	no	—
355	C₄²	C₂×C₃×D₄	1	4	yes	—
356	C₄²	C₂×C₃×D₄	1	2	yes	—
357	C₄²	C₂×C₃×D₄	1	4	yes	—
358	C₄²	C₂×C₃×D₄	1	2	yes	—
359	C₄²	C₂⁴×C₃	1	2	yes	—
360	C₄²	C₂⁴×C₃	1	2	yes	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	2	8	no	—
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	4	8	no	—
365	C₂²×C₃	—	4	8	no	—
366	C₂²×C₃	—	4	8	no	—
367	C₂²×C₃	—	8	32	no	—
368	C₂²×C₃	—	8	16	no	—
369	C₂²×C₃	#535	1	2	yes	—
370	C₂²×C₃	C₂²×SD₁₆	1	4	yes	—
371	C₂²×C₃	C₂²×SD₁₆	1	2	yes	—
372	C₂²×C₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
373	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	2	2	no	—
376	C₃×C₄	—	4	4	no	—
377	C₃×C₄	—	4	4	no	—
378	C₃×C₄	#535	1	2	yes	—
379	C₃×C₄	C₂²×SD₁₆	1	4	yes	—
380	C₃×C₄	C₂²×SD₁₆	1	4	yes	—
381	C₃×C₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
382	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	8	no	—
386	C₂³	—	4	16	no	—
387	C₂³	—	4	16	no	—
388	C₂³	—	4	16	no	—
389	C₂³	—	4	8	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	4	8	no	—
392	C₂³	—	8	32	no	—
393	C₂³	C₂×C₃×SD₁₆	1	4	yes	—
394	C₂³	C₂²×C₃×D₄	1	2	yes	—
395	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
396	Q₈	—	2	8	no	—
397	Q₈	—	4	8	no	—
398	Q₈	—	4	4	no	—
399	D₄	—	2	16	no	—
400	D₄	—	4	16	no	—
401	D₄	—	4	16	no	—
402	D₄	—	4	16	no	—
403	D₄	—	4	16	no	—
404	D₄	—	4	16	no	—
405	D₄	—	4	8	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	C₂×C₃×SD₁₆	1	4	yes	—
416	C₂×C₄	C₂×C₃×SD₁₆	1	4	yes	—
417	C₂×C₄	C₂×C₃×SD₁₆	1	16	yes	complemented
418	C₂×C₄	C₃×AGL(1,ℤ/8)	1	4	yes	—
419	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
420	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
421	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
422	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
423	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
424	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
425	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
426	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
427	C₈	—	2	8	no	—
428	C₂×C₃	—	2	4	no	—
429	C₂×C₃	—	8	8	no	—
430	C₂×C₃	#3208	1	4	yes	direct product factor
431	C₂×C₃	C₂×#535	1	1	yes	characteristic
432	C₂×C₃	C₂³×SD₁₆	1	1	yes	characteristic
433	C₂×C₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
434	C₂²	—	2	2	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	8	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	4	8	no	—
440	C₂²	—	8	32	no	—
441	C₂²	—	8	16	no	—
442	C₂²	C₃×#535	1	2	yes	—
443	C₂²	C₂²×C₃×SD₁₆	1	4	yes	—
444	C₂²	C₂²×C₃×SD₁₆	1	2	yes	—
445	C₂²	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
446	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	C₃×#535	1	2	yes	—
452	C₄	C₂²×C₃×SD₁₆	1	4	yes	—
453	C₄	C₂²×C₃×SD₁₆	1	4	yes	—
454	C₄	C₂×C₃×AGL(1,ℤ/8)	1	4	yes	—
455	C₄	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
456	C₃	C₂×#3208	1	1	yes	characteristic, direct product factor, Sylow
457	C₂	—	2	4	no	—
458	C₂	—	8	8	no	—
459	C₂	C₃×#3208	1	4	yes	direct product factor
460	C₂	C₂×C₃×#535	1	1	yes	characteristic
461	C₂	C₂³×C₃×SD₁₆	1	1	yes	characteristic
462	C₂	C₂²×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂²×C₃×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#533	C₂	semidirect
3. C₃×#3208	C₂	direct (N × H)
4. C₂×C₃×#492	C₂	semidirect
5. C₂×C₃×#486	C₂	semidirect
6. C₂×C₃×#460	C₂	semidirect
7. C₂×C₃×#450	C₂	semidirect
8. C₂×C₃×#431	C₂	semidirect
9. C₂×#3208	C₃	direct (N × H)
13. C₂²×C₃×SD₁₆	C₂²	semidirect
15. C₃×#533	C₂²	semidirect
16. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
17. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₃×C₄×Q₈	C₂²	semidirect
31. C₃×#492	C₂²	semidirect
32. C₃×#486	C₂²	semidirect
33. C₃×#460	C₂²	semidirect
34. C₃×#450	C₂²	semidirect
35. C₃×#431	C₂²	semidirect
36. C₂×C₃×C₄⋊C₈	C₂²	semidirect
37. C₂×C₃×#102	C₂²	semidirect
39. C₂×C₃×C₄×C₈	C₂²	semidirect
40. C₂×#533	C₂×C₃	semidirect
42. #3208	C₂×C₃	direct (N × H)
43. C₂×#492	C₂×C₃	semidirect
44. C₂×#486	C₂×C₃	semidirect
45. C₂×#460	C₂×C₃	semidirect
46. C₂×#450	C₂×C₃	semidirect
47. C₂×#431	C₂×C₃	semidirect
68. C₂×C₃×SD₁₆	C₂³	semidirect
72. C₃×C₄⋊Q₈	C₂³	semidirect
73. C₃×C₄⋊Q₈	C₂³	semidirect
86. C₃×C₄×Q₈	C₂³	semidirect
102. C₃×C₄⋊C₈	C₂³	semidirect
103. C₃×#102	C₂³	semidirect
105. C₃×C₄×C₈	C₂³	semidirect
109. C₂²×SD₁₆	C₂²×C₃	semidirect
111. #533	C₂²×C₃	semidirect
112. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
113. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
124. C₂×C₄×Q₈	C₂²×C₃	semidirect
127. #492	C₂²×C₃	semidirect
128. #486	C₂²×C₃	semidirect
129. #460	C₂²×C₃	semidirect
130. #450	C₂²×C₃	semidirect
131. #431	C₂²×C₃	semidirect
132. C₂×C₄⋊C₈	C₂²×C₃	semidirect
133. C₂×#102	C₂²×C₃	semidirect
135. C₂×C₄×C₈	C₂²×C₃	semidirect
168. C₂²×C₃×C₄	SD₁₆	semidirect
217. C₂×SD₁₆	C₂³×C₃	semidirect
221. C₄⋊Q₈	C₂³×C₃	semidirect
222. C₄⋊Q₈	C₂³×C₃	semidirect
235. C₄×Q₈	C₂³×C₃	semidirect
251. C₄⋊C₈	C₂³×C₃	semidirect
252. #102	C₂³×C₃	semidirect
254. C₄×C₈	C₂³×C₃	semidirect
289. C₂×C₃×C₄	C₂×SD₁₆	semidirect
332. C₂²×C₄	C₃×SD₁₆	semidirect
417. C₂×C₄	C₂×C₃×SD₁₆	semidirect
430. C₂×C₃	#3208	direct (N × H)
456. C₃	C₂×#3208	direct (N × H)
459. C₂	C₃×#3208	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×C₃×#533	2
C₂²×C₃×#127	2
C₃×#3208	2
C₂×C₃×#492	2
C₂×C₃×#486	2
C₂×C₃×#460	2
C₂×C₃×#450	2
C₂×C₃×#431	2
C₂×#3208	3

Subgroups — C2×C3×#3208 #10679382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3208 #10679382