Subgroups — C₂²×#6503⋊C₃ #72230194

Order 2688.

6000 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×(C₂²⋊D₇)⋊C₃	C₂	1	4	yes	maximal, complemented
3	C₂³×C₄⋊AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#6503⋊C₃	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₄×ΓL(1,𝔽₈)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6503	C₃	1	1	yes	maximal, characteristic, complemented, Hall
7	C₂⁵×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
8	C₂⁴×AGL(1,𝔽₇)	C₂²	1	2	yes	—
9	C₂²×D₄×ΓL(1,𝔽₈)	—	2	8	no	—
10	C₂²×D₄×ΓL(1,𝔽₈)	C₂²	1	12	yes	complemented
11	C₂³×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
12	C₂²×(C₂²⋊D₇)⋊C₃	—	2	32	no	—
13	C₂²×(C₂²⋊D₇)⋊C₃	C₂²	1	48	yes	complemented
14	C₂³×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₄⋊AGL(1,𝔽₇)	—	2	8	no	—
16	C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	1	12	yes	complemented
17	#6503⋊C₃	C₂²	1	64	yes	direct product factor
18	C₂×C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	12	yes	complemented
19	C₂³×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
20	C₂³×C₂²⋊D₇	C₂×C₃	1	4	yes	complemented
21	C₂³×D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×#6503	C₂×C₃	1	24	yes	complemented
23	C₂²×C₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×C₃×#127	—	7	1	no	maximal, Hall
25	C₂⁴×ΓL(1,𝔽₈)	—	2	8	no	—
26	C₂⁴×ΓL(1,𝔽₈)	—	2	16	no	—
27	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	12	yes	—
28	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
29	C₂³×AGL(1,𝔽₇)	—	2	8	no	—
30	C₂³×AGL(1,𝔽₇)	—	2	16	no	—
31	C₂³×AGL(1,𝔽₇)	C₂³	1	12	yes	—
32	C₂×D₄×ΓL(1,𝔽₈)	—	2	48	no	—
33	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	16	yes	complemented
34	C₂²×C₄×ΓL(1,𝔽₈)	D₄	1	8	yes	complemented
35	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	6	yes	—
36	C₂×(C₂²⋊D₇)⋊C₃	—	2	192	no	—
37	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	64	yes	complemented
38	C₂²×ΓL(1,𝔽₈)⋊C₄	D₄	1	16	yes	complemented
39	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	1	12	yes	—
40	C₂×C₄⋊AGL(1,𝔽₇)	—	2	48	no	—
41	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	16	yes	complemented
42	C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	1	16	yes	complemented
43	C₂⁵×C₇	C₂²×C₃	1	2	yes	—
44	C₂⁴×D₇	C₂²×C₃	1	2	yes	—
45	C₂²×C₇×D₄	—	2	8	no	—
46	C₂²×C₇×D₄	C₂²×C₃	1	12	yes	complemented
47	C₂³×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₂²⋊D₇	—	2	32	no	—
49	C₂²×C₂²⋊D₇	C₂²×C₃	1	48	yes	complemented
50	C₂³×Dic₇	C₂²×C₃	1	2	yes	—
51	C₂²×D₂₈	—	2	8	no	—
52	C₂²×D₂₈	C₂²×C₃	1	12	yes	complemented
53	#6503	C₂²×C₃	1	64	yes	complemented
54	C₂×C₄×Dic₇	C₂²×C₃	1	12	yes	complemented
55	C₂³×C₃×D₄	—	7	1	no	—
56	C₂³×C₃×D₄	—	7	4	no	—
57	C₂³×C₃×D₄	—	14	1	no	—
58	C₂×C₃×#127	—	7	24	no	—
59	C₂²×C₃×C₄²	—	7	1	no	—
60	C₂³×ΓL(1,𝔽₈)	—	2	24	no	—
61	C₂³×ΓL(1,𝔽₈)	—	2	48	no	—
62	C₂³×ΓL(1,𝔽₈)	—	4	32	no	—
63	C₂³×ΓL(1,𝔽₈)	C₂×D₄	1	8	yes	—
64	C₂³×ΓL(1,𝔽₈)	C₂×D₄	1	4	yes	—
65	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	8	yes	—
66	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	3	yes	—
67	C₂²×AGL(1,𝔽₇)	—	2	24	no	—
68	C₂²×AGL(1,𝔽₇)	—	2	48	no	—
69	C₂²×AGL(1,𝔽₇)	—	4	32	no	—
70	C₂²×AGL(1,𝔽₇)	C₂⁴	1	8	yes	—
71	D₄×ΓL(1,𝔽₈)	—	2	32	no	—
72	C₂×C₄×ΓL(1,𝔽₈)	C₂×D₄	1	24	yes	complemented
73	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	4	yes	—
74	(C₂²⋊D₇)⋊C₃	—	2	128	no	—
75	C₂×ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	48	yes	complemented
76	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	8	yes	—
77	C₄⋊AGL(1,𝔽₇)	—	2	32	no	—
78	C₂²×#127	—	7	1	no	Sylow
79	C₂⁴×C₇	—	2	16	no	—
80	C₂⁴×C₇	—	2	8	no	—
81	C₂⁴×C₇	C₂³×C₃	1	12	yes	—
82	C₂⁴×C₇	C₂³×C₃	1	1	yes	characteristic
83	C₂³×D₇	—	2	8	no	—
84	C₂³×D₇	—	2	16	no	—
85	C₂³×D₇	C₂³×C₃	1	12	yes	—
86	C₂×C₇×D₄	—	2	48	no	—
87	C₂×C₇×D₄	C₂³×C₃	1	16	yes	complemented
88	C₂²×C₄×C₇	C₃×D₄	1	8	yes	complemented
89	C₂²×C₄×C₇	C₂³×C₃	1	6	yes	—
90	C₂×C₂²⋊D₇	—	2	192	no	—
91	C₂×C₂²⋊D₇	C₂³×C₃	1	64	yes	complemented
92	C₂²×Dic₇	C₃×D₄	1	16	yes	complemented
93	C₂²×Dic₇	C₂³×C₃	1	12	yes	—
94	C₂×D₂₈	—	2	48	no	—
95	C₂×D₂₈	C₂³×C₃	1	16	yes	complemented
96	C₄×Dic₇	C₂³×C₃	1	16	yes	complemented
97	C₂⁵×C₃	—	7	2	no	—
98	C₂⁵×C₃	—	14	2	no	—
99	C₂²×C₃×D₄	—	7	48	no	—
100	C₂²×C₃×D₄	—	7	12	no	—
101	C₂²×C₃×D₄	—	14	8	no	—
102	C₂²×C₃×D₄	—	14	32	no	—
103	C₂²×C₃×D₄	—	14	8	no	—
104	C₂²×C₃×D₄	—	14	12	no	—
105	C₂³×C₃×C₄	—	7	2	no	—
106	C₂³×C₃×C₄	—	14	1	no	—
107	C₃×#127	—	7	64	no	—
108	C₂×C₃×C₄²	—	7	12	no	—
109	C₂²×ΓL(1,𝔽₈)	—	2	8	no	—
110	C₂²×ΓL(1,𝔽₈)	—	2	16	no	—
111	C₂²×ΓL(1,𝔽₈)	—	4	48	no	—
112	C₂²×ΓL(1,𝔽₈)	#127	1	16	yes	complemented
113	C₂²×ΓL(1,𝔽₈)	C₂²×D₄	1	12	yes	—
114	C₂²×ΓL(1,𝔽₈)	C₂²×D₄	1	6	yes	—
115	C₂²×ΓL(1,𝔽₈)	C₂⁵	1	1	yes	characteristic
116	C₂×AGL(1,𝔽₇)	—	2	8	no	—
117	C₂×AGL(1,𝔽₇)	—	2	16	no	—
118	C₂×AGL(1,𝔽₇)	—	4	48	no	—
119	C₄×ΓL(1,𝔽₈)	C₂²×D₄	1	8	yes	complemented
120	ΓL(1,𝔽₈)⋊C₄	C₂²×D₄	1	16	yes	complemented
121	C₂³×D₄	—	7	4	no	—
122	C₂³×D₄	—	7	1	no	—
123	C₂³×D₄	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
124	C₂×#127	—	7	24	no	—
125	C₂²×C₄²	—	7	1	no	—
126	C₂³×C₇	—	2	48	no	—
127	C₂³×C₇	—	2	24	no	—
128	C₂³×C₇	—	4	32	no	—
129	C₂³×C₇	C₂×C₃×D₄	1	8	yes	—
130	C₂³×C₇	C₂×C₃×D₄	1	4	yes	—
131	C₂³×C₇	C₂⁴×C₃	1	8	yes	—
132	C₂³×C₇	C₂⁴×C₃	1	3	yes	—
133	C₂²×D₇	—	2	24	no	—
134	C₂²×D₇	—	2	48	no	—
135	C₂²×D₇	—	4	32	no	—
136	C₂²×D₇	C₂⁴×C₃	1	8	yes	—
137	C₇×D₄	—	2	32	no	—
138	C₂×C₄×C₇	C₂×C₃×D₄	1	24	yes	complemented
139	C₂×C₄×C₇	C₂⁴×C₃	1	4	yes	—
140	C₂²⋊D₇	—	2	128	no	—
141	C₂×Dic₇	C₂×C₃×D₄	1	48	yes	complemented
142	C₂×Dic₇	C₂⁴×C₃	1	8	yes	—
143	D₂₈	—	2	32	no	—
144	C₂⁴×C₃	—	7	12	no	—
145	C₂⁴×C₃	—	14	8	no	—
146	C₂⁴×C₃	—	14	16	no	—
147	C₂⁴×C₃	—	14	8	no	—
148	C₂⁴×C₃	—	14	12	no	—
149	C₂⁴×C₃	—	14	1	no	—
150	C₂⁴×C₃	—	28	16	no	—
151	C₂×C₃×D₄	—	7	64	no	—
152	C₂×C₃×D₄	—	7	16	no	—
153	C₂×C₃×D₄	—	14	48	no	—
154	C₂×C₃×D₄	—	14	192	no	—
155	C₂×C₃×D₄	—	14	48	no	—
156	C₂×C₃×D₄	—	14	16	no	—
157	C₂²×C₃×C₄	—	7	16	no	—
158	C₂²×C₃×C₄	—	7	12	no	—
159	C₂²×C₃×C₄	—	14	8	no	—
160	C₂²×C₃×C₄	—	14	6	no	—
161	C₃×C₄²	—	7	16	no	—
162	C₂×ΓL(1,𝔽₈)	—	4	8	no	—
163	C₂×ΓL(1,𝔽₈)	C₂×#127	1	12	yes	complemented
164	C₂×ΓL(1,𝔽₈)	C₂³×D₄	1	2	yes	—
165	C₂×ΓL(1,𝔽₈)	C₂³×D₄	1	1	yes	characteristic
166	AGL(1,𝔽₇)	—	4	8	no	—
167	C₂⁵	—	7	2	no	—
168	C₂⁵	C₂×AGL(1,𝔽₇)	1	2	yes	—
169	C₂²×D₄	—	2	8	no	—
170	C₂²×D₄	—	7	48	no	—
171	C₂²×D₄	—	7	12	no	—
172	C₂²×D₄	—	14	32	no	—
173	C₂²×D₄	—	14	8	no	—
174	C₂²×D₄	C₂×AGL(1,𝔽₇)	1	12	yes	complemented
175	C₂³×C₄	—	7	2	no	—
176	C₂³×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
177	#127	—	7	64	no	—
178	C₂×C₄²	—	7	12	no	—
179	C₂²×C₇	—	2	16	no	—
180	C₂²×C₇	—	2	8	no	—
181	C₂²×C₇	—	4	48	no	—
182	C₂²×C₇	C₃×#127	1	16	yes	complemented
183	C₂²×C₇	C₂²×C₃×D₄	1	12	yes	—
184	C₂²×C₇	C₂²×C₃×D₄	1	6	yes	—
185	C₂²×C₇	C₂⁵×C₃	1	1	yes	characteristic
186	C₂×D₇	—	2	8	no	—
187	C₂×D₇	—	2	16	no	—
188	C₂×D₇	—	4	48	no	—
189	C₄×C₇	C₂²×C₃×D₄	1	8	yes	complemented
190	Dic₇	C₂²×C₃×D₄	1	16	yes	complemented
191	C₂³×C₃	—	7	8	no	—
192	C₂³×C₃	—	14	24	no	—
193	C₂³×C₃	—	14	48	no	—
194	C₂³×C₃	—	14	24	no	—
195	C₂³×C₃	—	14	8	no	—
196	C₂³×C₃	—	14	4	no	—
197	C₂³×C₃	—	14	3	no	—
198	C₂³×C₃	—	14	8	no	—
199	C₂³×C₃	—	28	48	no	—
200	C₂³×C₃	—	28	32	no	—
201	C₂³×C₃	—	28	32	no	—
202	C₃×D₄	—	14	32	no	—
203	C₃×D₄	—	14	128	no	—
204	C₃×D₄	—	14	32	no	—
205	C₂×C₃×C₄	—	7	48	no	—
206	C₂×C₃×C₄	—	7	8	no	—
207	C₂×C₃×C₄	—	14	24	no	—
208	C₂×C₃×C₄	—	14	4	no	—
209	ΓL(1,𝔽₈)	C₂²×#127	1	1	yes	characteristic, complemented, Hall
210	C₂⁴	—	2	16	no	—
211	C₂⁴	—	2	8	no	—
212	C₂⁴	—	7	12	no	—
213	C₂⁴	—	14	16	no	—
214	C₂⁴	—	14	8	no	—
215	C₂⁴	C₂²×AGL(1,𝔽₇)	1	12	yes	—
216	C₂⁴	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
217	C₂×D₄	—	2	48	no	—
218	C₂×D₄	—	7	64	no	—
219	C₂×D₄	—	7	16	no	—
220	C₂×D₄	—	14	192	no	—
221	C₂×D₄	—	14	48	no	—
222	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	16	yes	complemented
223	C₂²×C₄	—	7	16	no	—
224	C₂²×C₄	—	7	12	no	—
225	C₂²×C₄	(C₂²⋊D₇)⋊C₃	1	8	yes	complemented
226	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	6	yes	—
227	C₄²	—	7	16	no	—
228	C₂×C₇	—	4	8	no	—
229	C₂×C₇	C₂×C₃×#127	1	12	yes	complemented
230	C₂×C₇	C₂³×C₃×D₄	1	2	yes	—
231	C₂×C₇	C₂³×C₃×D₄	1	1	yes	characteristic
232	D₇	—	4	8	no	—
233	C₂²×C₃	—	14	8	no	—
234	C₂²×C₃	—	14	16	no	—
235	C₂²×C₃	—	14	8	no	—
236	C₂²×C₃	—	14	12	no	—
237	C₂²×C₃	—	14	6	no	—
238	C₂²×C₃	—	14	16	no	—
239	C₂²×C₃	—	14	1	no	—
240	C₂²×C₃	—	28	16	no	—
241	C₂²×C₃	—	28	48	no	—
242	C₂²×C₃	—	28	48	no	—
243	C₃×C₄	—	7	16	no	—
244	C₃×C₄	—	14	8	no	—
245	C₂³	—	2	48	no	—
246	C₂³	—	2	24	no	—
247	C₂³	—	4	32	no	—
248	C₂³	—	7	8	no	—
249	C₂³	—	14	48	no	—
250	C₂³	—	14	24	no	—
251	C₂³	—	28	32	no	—
252	C₂³	D₄×AGL(1,𝔽₇)	1	8	yes	—
253	C₂³	C₂×(C₂²⋊D₇)⋊C₃	1	4	yes	—
254	C₂³	C₂³×AGL(1,𝔽₇)	1	8	yes	—
255	C₂³	C₂³×AGL(1,𝔽₇)	1	3	yes	—
256	D₄	—	2	32	no	—
257	D₄	—	14	128	no	—
258	D₄	—	14	32	no	—
259	C₂×C₄	—	7	48	no	—
260	C₂×C₄	—	7	8	no	—
261	C₂×C₄	C₂×(C₂²⋊D₇)⋊C₃	1	24	yes	complemented
262	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	4	yes	—
263	C₇	C₂²×C₃×#127	1	1	yes	characteristic, complemented, Sylow
264	C₂×C₃	—	14	2	no	—
265	C₂×C₃	—	14	1	no	—
266	C₂×C₃	—	14	12	no	—
267	C₂×C₃	—	28	8	no	—
268	C₂×C₃	—	28	8	no	—
269	C₂²	—	2	16	no	—
270	C₂²	—	2	8	no	—
271	C₂²	—	4	48	no	—
272	C₂²	—	14	16	no	—
273	C₂²	—	14	8	no	—
274	C₂²	—	28	48	no	—
275	C₂²	#6503⋊C₃	1	16	yes	direct product factor
276	C₂²	C₂×D₄×AGL(1,𝔽₇)	1	12	yes	—
277	C₂²	C₂²×(C₂²⋊D₇)⋊C₃	1	6	yes	—
278	C₂²	C₂⁴×AGL(1,𝔽₇)	1	1	yes	characteristic
279	C₄	—	7	16	no	—
280	C₄	C₂²×(C₂²⋊D₇)⋊C₃	1	8	yes	complemented
281	C₃	—	14	1	no	Sylow
282	C₂	—	4	8	no	—
283	C₂	—	28	8	no	—
284	C₂	C₂×#6503⋊C₃	1	12	yes	direct product factor
285	C₂	C₂²×D₄×AGL(1,𝔽₇)	1	2	yes	—
286	C₂	C₂³×(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²×AGL(1,𝔽₇)
commutator, cosocle	C₂²×C₇	C₂⁵×C₃
Frattini	C₂²	C₂⁴×AGL(1,𝔽₇)
Fitting	C₂³×C₇×D₄	C₂×C₃
socle	C₂⁴×C₇	C₂³×C₃
hypercenter	C₂³×D₄	AGL(1,𝔽₇)
hypocenter	C₇	C₂²×C₃×#127
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×ΓL(1,𝔽₈)	C₂	semidirect
2. C₂³×(C₂²⋊D₇)⋊C₃	C₂	semidirect
3. C₂³×C₄⋊AGL(1,𝔽₇)	C₂	semidirect
4. C₂×#6503⋊C₃	C₂	direct (N × H)
5. C₂²×C₄×ΓL(1,𝔽₈)⋊C₄	C₂	semidirect
6. C₂²×#6503	C₃	semidirect
10. C₂²×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
13. C₂²×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
16. C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
17. #6503⋊C₃	C₂²	direct (N × H)
18. C₂×C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
19. C₂³×C₇×D₄	C₂×C₃	semidirect
20. C₂³×C₂²⋊D₇	C₂×C₃	semidirect
21. C₂³×D₂₈	C₂×C₃	semidirect
22. C₂×#6503	C₂×C₃	semidirect
23. C₂²×C₄×Dic₇	C₂×C₃	semidirect
33. C₂×D₄×ΓL(1,𝔽₈)	C₂³	semidirect
34. C₂²×C₄×ΓL(1,𝔽₈)	D₄	semidirect
37. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
38. C₂²×ΓL(1,𝔽₈)⋊C₄	D₄	semidirect
41. C₂×C₄⋊AGL(1,𝔽₇)	C₂³	semidirect
42. C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
46. C₂²×C₇×D₄	C₂²×C₃	semidirect
49. C₂²×C₂²⋊D₇	C₂²×C₃	semidirect
52. C₂²×D₂₈	C₂²×C₃	semidirect
53. #6503	C₂²×C₃	semidirect
54. C₂×C₄×Dic₇	C₂²×C₃	semidirect
72. C₂×C₄×ΓL(1,𝔽₈)	C₂×D₄	semidirect
75. C₂×ΓL(1,𝔽₈)⋊C₄	C₂×D₄	semidirect
87. C₂×C₇×D₄	C₂³×C₃	semidirect
88. C₂²×C₄×C₇	C₃×D₄	semidirect
91. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
92. C₂²×Dic₇	C₃×D₄	semidirect
95. C₂×D₂₈	C₂³×C₃	semidirect
96. C₄×Dic₇	C₂³×C₃	semidirect
112. C₂²×ΓL(1,𝔽₈)	#127	semidirect
119. C₄×ΓL(1,𝔽₈)	C₂²×D₄	semidirect
120. ΓL(1,𝔽₈)⋊C₄	C₂²×D₄	semidirect
123. C₂³×D₄	AGL(1,𝔽₇)	semidirect
138. C₂×C₄×C₇	C₂×C₃×D₄	semidirect
141. C₂×Dic₇	C₂×C₃×D₄	semidirect
163. C₂×ΓL(1,𝔽₈)	C₂×#127	semidirect
174. C₂²×D₄	C₂×AGL(1,𝔽₇)	semidirect
182. C₂²×C₇	C₃×#127	semidirect
189. C₄×C₇	C₂²×C₃×D₄	semidirect
190. Dic₇	C₂²×C₃×D₄	semidirect
209. ΓL(1,𝔽₈)	C₂²×#127	semidirect
222. C₂×D₄	C₂²×AGL(1,𝔽₇)	semidirect
225. C₂²×C₄	(C₂²⋊D₇)⋊C₃	semidirect
229. C₂×C₇	C₂×C₃×#127	semidirect
261. C₂×C₄	C₂×(C₂²⋊D₇)⋊C₃	semidirect
263. C₇	C₂²×C₃×#127	semidirect
275. C₂²	#6503⋊C₃	direct (N × H)
280. C₄	C₂²×(C₂²⋊D₇)⋊C₃	semidirect
284. C₂	C₂×#6503⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×ΓL(1,𝔽₈)	2
C₂³×(C₂²⋊D₇)⋊C₃	2
C₂³×C₄⋊AGL(1,𝔽₇)	2
C₂×#6503⋊C₃	2
C₂²×C₄×ΓL(1,𝔽₈)⋊C₄	2
C₂²×#6503	3
C₂²×C₃×#127	7

Subgroups — C22×#6503⋊C3 #72230194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#6503⋊C₃ #72230194