Subgroups — ΓL(1,𝔽₈)×#1438 #72230200

Order 2688.

2336 conjugacy classes of subgroups.

The subgroup lattice has 340 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
2	C₂²×C₂²⋊C₄×ΓL(1,𝔽₈)	C₂	1	4	yes	maximal, complemented
3	C₂×ΓL(1,𝔽₈)×#95	C₂	1	2	yes	maximal, complemented
4	C₇×#1438	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂⁵×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
6	C₂²×D₄×ΓL(1,𝔽₈)	—	2	8	no	—
7	C₂²×D₄×ΓL(1,𝔽₈)	—	2	4	no	—
8	C₂²×D₄×ΓL(1,𝔽₈)	C₄	1	4	yes	complemented
9	C₂³×C₄×ΓL(1,𝔽₈)	C₂²	1	4	yes	—
10	C₂³×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊C₄×ΓL(1,𝔽₈)	—	2	8	no	—
12	C₂×C₂²⋊C₄×ΓL(1,𝔽₈)	—	2	16	no	—
13	ΓL(1,𝔽₈)×#95	—	2	4	no	—
14	C₂³×C₇×D₄	C₂×C₃	1	1	yes	characteristic
15	C₂²×C₇×C₂²⋊C₄	C₂×C₃	1	4	yes	complemented
16	C₂×C₇×#95	C₂×C₃	1	2	yes	complemented
17	C₃×#1438	—	7	1	no	maximal, Hall
18	C₂⁴×ΓL(1,𝔽₈)	—	2	4	no	—
19	C₂⁴×ΓL(1,𝔽₈)	—	2	4	no	—
20	C₂⁴×ΓL(1,𝔽₈)	—	2	8	no	—
21	C₂⁴×ΓL(1,𝔽₈)	—	2	8	no	—
22	C₂⁴×ΓL(1,𝔽₈)	C₂×C₄	1	4	yes	—
23	C₂⁴×ΓL(1,𝔽₈)	D₄	1	8	yes	—
24	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
25	C₂×D₄×ΓL(1,𝔽₈)	—	2	32	no	—
26	C₂×D₄×ΓL(1,𝔽₈)	—	2	16	no	—
27	C₂×D₄×ΓL(1,𝔽₈)	—	2	8	no	—
28	C₂²×C₄×ΓL(1,𝔽₈)	—	2	4	no	—
29	C₂²×C₄×ΓL(1,𝔽₈)	—	2	4	no	—
30	C₂²×C₄×ΓL(1,𝔽₈)	—	2	8	no	—
31	C₂²×C₄×ΓL(1,𝔽₈)	—	2	8	no	—
32	C₂²×C₄×ΓL(1,𝔽₈)	—	2	4	no	—
33	C₂²×C₄×ΓL(1,𝔽₈)	C₂×C₄	1	2	yes	—
34	C₂²×C₄×ΓL(1,𝔽₈)	D₄	1	4	yes	—
35	C₂²×C₄×ΓL(1,𝔽₈)	D₄	1	8	yes	complemented
36	C₂²⋊C₄×ΓL(1,𝔽₈)	—	2	32	no	—
37	C₂⁵×C₇	C₂²×C₃	1	2	yes	—
38	C₂²×C₇×D₄	—	2	8	no	—
39	C₂²×C₇×D₄	—	2	4	no	—
40	C₂²×C₇×D₄	C₃×C₄	1	4	yes	complemented
41	C₂³×C₄×C₇	C₂²×C₃	1	4	yes	—
42	C₂³×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
43	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
44	C₂×C₇×C₂²⋊C₄	—	2	16	no	—
45	C₇×#95	—	2	4	no	—
46	C₂³×C₃×D₄	—	7	1	no	—
47	C₂²×C₃×C₂²⋊C₄	—	7	4	no	—
48	C₂×C₃×#95	—	7	2	no	—
49	C₂³×ΓL(1,𝔽₈)	—	2	4	no	—
50	C₂³×ΓL(1,𝔽₈)	—	2	4	no	—
51	C₂³×ΓL(1,𝔽₈)	—	2	16	no	—
52	C₂³×ΓL(1,𝔽₈)	—	2	8	no	—
53	C₂³×ΓL(1,𝔽₈)	—	2	16	no	—
54	C₂³×ΓL(1,𝔽₈)	—	2	16	no	—
55	C₂³×ΓL(1,𝔽₈)	—	2	8	no	—
56	C₂³×ΓL(1,𝔽₈)	—	4	4	no	—
57	C₂³×ΓL(1,𝔽₈)	—	4	8	no	—
58	C₂³×ΓL(1,𝔽₈)	—	4	8	no	—
59	C₂³×ΓL(1,𝔽₈)	—	4	4	no	—
60	C₂³×ΓL(1,𝔽₈)	—	4	4	no	—
61	C₂³×ΓL(1,𝔽₈)	—	4	4	no	—
62	C₂³×ΓL(1,𝔽₈)	C₂²⋊C₄	1	8	yes	complemented
63	C₂³×ΓL(1,𝔽₈)	C₂²×C₄	1	1	yes	characteristic
64	C₂³×ΓL(1,𝔽₈)	C₂×D₄	1	4	yes	—
65	C₂³×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	—
66	C₂³×ΓL(1,𝔽₈)	C₂×D₄	1	4	yes	—
67	C₂³×ΓL(1,𝔽₈)	#41	1	4	yes	—
68	D₄×ΓL(1,𝔽₈)	—	2	32	no	—
69	C₂×C₄×ΓL(1,𝔽₈)	—	2	4	no	—
70	C₂×C₄×ΓL(1,𝔽₈)	—	2	8	no	—
71	C₂×C₄×ΓL(1,𝔽₈)	—	2	16	no	—
72	C₂×C₄×ΓL(1,𝔽₈)	—	2	8	no	—
73	C₂×C₄×ΓL(1,𝔽₈)	—	4	4	no	—
74	C₂×C₄×ΓL(1,𝔽₈)	—	4	8	no	—
75	C₂×C₄×ΓL(1,𝔽₈)	—	4	4	no	—
76	C₂×C₄×ΓL(1,𝔽₈)	C₂²⋊C₄	1	4	yes	complemented
77	#1438	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow
78	C₂⁴×C₇	—	2	8	no	—
79	C₂⁴×C₇	—	2	4	no	—
80	C₂⁴×C₇	—	2	4	no	—
81	C₂⁴×C₇	—	2	8	no	—
82	C₂⁴×C₇	C₂×C₃×C₄	1	4	yes	—
83	C₂⁴×C₇	C₃×D₄	1	8	yes	—
84	C₂⁴×C₇	C₂³×C₃	1	1	yes	characteristic
85	C₂×C₇×D₄	—	2	32	no	—
86	C₂×C₇×D₄	—	2	16	no	—
87	C₂×C₇×D₄	—	2	8	no	—
88	C₂²×C₄×C₇	—	2	4	no	—
89	C₂²×C₄×C₇	—	2	4	no	—
90	C₂²×C₄×C₇	—	2	8	no	—
91	C₂²×C₄×C₇	—	2	8	no	—
92	C₂²×C₄×C₇	—	2	4	no	—
93	C₂²×C₄×C₇	C₂×C₃×C₄	1	2	yes	—
94	C₂²×C₄×C₇	C₃×D₄	1	4	yes	—
95	C₂²×C₄×C₇	C₃×D₄	1	8	yes	complemented
96	C₇×C₂²⋊C₄	—	2	32	no	—
97	C₂⁵×C₃	—	7	2	no	—
98	C₂²×C₃×D₄	—	7	4	no	—
99	C₂²×C₃×D₄	—	14	4	no	—
100	C₂²×C₃×D₄	—	14	8	no	—
101	C₂³×C₃×C₄	—	7	1	no	—
102	C₂³×C₃×C₄	—	7	4	no	—
103	C₂×C₃×C₂²⋊C₄	—	14	16	no	—
104	C₂×C₃×C₂²⋊C₄	—	14	8	no	—
105	C₃×#95	—	14	4	no	—
106	C₂²×ΓL(1,𝔽₈)	—	2	8	no	—
107	C₂²×ΓL(1,𝔽₈)	—	2	16	no	—
108	C₂²×ΓL(1,𝔽₈)	—	4	8	no	—
109	C₂²×ΓL(1,𝔽₈)	—	4	8	no	—
110	C₂²×ΓL(1,𝔽₈)	—	4	16	no	—
111	C₂²×ΓL(1,𝔽₈)	—	4	16	no	—
112	C₂²×ΓL(1,𝔽₈)	C₂×C₂²⋊C₄	1	2	yes	—
113	C₂²×ΓL(1,𝔽₈)	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×ΓL(1,𝔽₈)	C₄×D₄	1	4	yes	—
115	C₂²×ΓL(1,𝔽₈)	#120	1	4	yes	—
116	C₂²×ΓL(1,𝔽₈)	#120	1	4	yes	—
117	C₂²×ΓL(1,𝔽₈)	#121	1	8	yes	—
118	C₂²×ΓL(1,𝔽₈)	#121	1	4	yes	—
119	C₂²×ΓL(1,𝔽₈)	#123	1	4	yes	—
120	C₂²×ΓL(1,𝔽₈)	#124	1	2	yes	—
121	C₂²×ΓL(1,𝔽₈)	#127	1	2	yes	—
122	C₄×ΓL(1,𝔽₈)	—	2	4	no	—
123	C₄×ΓL(1,𝔽₈)	—	4	8	no	—
124	C₂³×D₄	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
125	C₂²×C₂²⋊C₄	C₂×ΓL(1,𝔽₈)	1	4	yes	complemented
126	C₂×#95	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
127	C₂³×C₇	—	2	4	no	—
128	C₂³×C₇	—	2	4	no	—
129	C₂³×C₇	—	2	16	no	—
130	C₂³×C₇	—	2	8	no	—
131	C₂³×C₇	—	2	16	no	—
132	C₂³×C₇	—	2	16	no	—
133	C₂³×C₇	—	2	8	no	—
134	C₂³×C₇	—	4	4	no	—
135	C₂³×C₇	—	4	8	no	—
136	C₂³×C₇	—	4	8	no	—
137	C₂³×C₇	—	4	4	no	—
138	C₂³×C₇	—	4	4	no	—
139	C₂³×C₇	—	4	4	no	—
140	C₂³×C₇	C₃×C₂²⋊C₄	1	8	yes	complemented
141	C₂³×C₇	C₂²×C₃×C₄	1	1	yes	characteristic
142	C₂³×C₇	C₂×C₃×D₄	1	4	yes	—
143	C₂³×C₇	C₂×C₃×D₄	1	2	yes	—
144	C₂³×C₇	C₂×C₃×D₄	1	4	yes	—
145	C₂³×C₇	C₃×#41	1	4	yes	—
146	C₇×D₄	—	2	32	no	—
147	C₂×C₄×C₇	—	2	4	no	—
148	C₂×C₄×C₇	—	2	8	no	—
149	C₂×C₄×C₇	—	2	16	no	—
150	C₂×C₄×C₇	—	2	8	no	—
151	C₂×C₄×C₇	—	4	4	no	—
152	C₂×C₄×C₇	—	4	8	no	—
153	C₂×C₄×C₇	—	4	4	no	—
154	C₂×C₄×C₇	C₃×C₂²⋊C₄	1	4	yes	complemented
155	C₂⁴×C₃	—	7	4	no	—
156	C₂⁴×C₃	—	7	8	no	—
157	C₂⁴×C₃	—	7	1	no	—
158	C₂⁴×C₃	—	14	8	no	—
159	C₂⁴×C₃	—	14	8	no	—
160	C₂⁴×C₃	—	14	4	no	—
161	C₂⁴×C₃	—	14	4	no	—
162	C₂×C₃×D₄	—	14	8	no	—
163	C₂×C₃×D₄	—	14	16	no	—
164	C₂×C₃×D₄	—	14	32	no	—
165	C₂²×C₃×C₄	—	7	2	no	—
166	C₂²×C₃×C₄	—	7	4	no	—
167	C₂²×C₃×C₄	—	7	8	no	—
168	C₂²×C₃×C₄	—	14	4	no	—
169	C₂²×C₃×C₄	—	14	4	no	—
170	C₂²×C₃×C₄	—	14	8	no	—
171	C₂²×C₃×C₄	—	14	8	no	—
172	C₂²×C₃×C₄	—	14	4	no	—
173	C₃×C₂²⋊C₄	—	14	32	no	—
174	C₂×ΓL(1,𝔽₈)	—	4	8	no	—
175	C₂×ΓL(1,𝔽₈)	#379	1	1	yes	characteristic
176	C₂×ΓL(1,𝔽₈)	#386	1	4	yes	—
177	C₂×ΓL(1,𝔽₈)	#390	1	2	yes	—
178	C₂×ΓL(1,𝔽₈)	#392	1	4	yes	—
179	C₂×ΓL(1,𝔽₈)	#394	1	4	yes	—
180	C₂⁵	C₂²×ΓL(1,𝔽₈)	1	2	yes	—
181	C₂²×D₄	—	2	8	no	—
182	C₂²×D₄	—	2	4	no	—
183	C₂²×D₄	C₄×ΓL(1,𝔽₈)	1	4	yes	complemented
184	C₂³×C₄	C₂²×ΓL(1,𝔽₈)	1	4	yes	—
185	C₂³×C₄	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
186	C₂×C₂²⋊C₄	—	2	8	no	—
187	C₂×C₂²⋊C₄	—	2	16	no	—
188	#95	—	2	4	no	—
189	C₂²×C₇	—	2	8	no	—
190	C₂²×C₇	—	2	16	no	—
191	C₂²×C₇	—	4	8	no	—
192	C₂²×C₇	—	4	8	no	—
193	C₂²×C₇	—	4	16	no	—
194	C₂²×C₇	—	4	16	no	—
195	C₂²×C₇	C₂×C₃×C₂²⋊C₄	1	2	yes	—
196	C₂²×C₇	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₇	C₃×C₄×D₄	1	4	yes	—
198	C₂²×C₇	C₃×#120	1	4	yes	—
199	C₂²×C₇	C₃×#120	1	4	yes	—
200	C₂²×C₇	C₃×#121	1	8	yes	—
201	C₂²×C₇	C₃×#121	1	4	yes	—
202	C₂²×C₇	C₃×#123	1	4	yes	—
203	C₂²×C₇	C₃×#124	1	2	yes	—
204	C₂²×C₇	C₃×#127	1	2	yes	—
205	C₄×C₇	—	2	4	no	—
206	C₄×C₇	—	4	8	no	—
207	C₂³×C₃	—	7	8	no	—
208	C₂³×C₃	—	7	1	no	—
209	C₂³×C₃	—	7	2	no	—
210	C₂³×C₃	—	7	4	no	—
211	C₂³×C₃	—	7	4	no	—
212	C₂³×C₃	—	7	4	no	—
213	C₂³×C₃	—	14	8	no	—
214	C₂³×C₃	—	14	4	no	—
215	C₂³×C₃	—	14	4	no	—
216	C₂³×C₃	—	14	16	no	—
217	C₂³×C₃	—	14	16	no	—
218	C₂³×C₃	—	14	16	no	—
219	C₂³×C₃	—	14	8	no	—
220	C₂³×C₃	—	28	4	no	—
221	C₂³×C₃	—	28	8	no	—
222	C₂³×C₃	—	28	8	no	—
223	C₂³×C₃	—	28	4	no	—
224	C₂³×C₃	—	28	4	no	—
225	C₂³×C₃	—	28	4	no	—
226	C₃×D₄	—	14	32	no	—
227	C₂×C₃×C₄	—	7	4	no	—
228	C₂×C₃×C₄	—	14	4	no	—
229	C₂×C₃×C₄	—	14	8	no	—
230	C₂×C₃×C₄	—	14	16	no	—
231	C₂×C₃×C₄	—	14	8	no	—
232	C₂×C₃×C₄	—	28	4	no	—
233	C₂×C₃×C₄	—	28	8	no	—
234	C₂×C₃×C₄	—	28	4	no	—
235	ΓL(1,𝔽₈)	#1438	1	1	yes	characteristic, direct product factor, Hall
236	C₂⁴	—	2	8	no	—
237	C₂⁴	—	2	4	no	—
238	C₂⁴	—	2	4	no	—
239	C₂⁴	—	2	8	no	—
240	C₂⁴	C₂×C₄×ΓL(1,𝔽₈)	1	4	yes	—
241	C₂⁴	D₄×ΓL(1,𝔽₈)	1	8	yes	—
242	C₂⁴	C₂³×ΓL(1,𝔽₈)	1	1	yes	characteristic
243	C₂×D₄	—	2	32	no	—
244	C₂×D₄	—	2	16	no	—
245	C₂×D₄	—	2	8	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	C₂×C₄×ΓL(1,𝔽₈)	1	2	yes	—
252	C₂²×C₄	D₄×ΓL(1,𝔽₈)	1	4	yes	—
253	C₂²×C₄	D₄×ΓL(1,𝔽₈)	1	8	yes	complemented
254	C₂²⋊C₄	—	2	32	no	—
255	C₂×C₇	—	4	8	no	—
256	C₂×C₇	C₃×#379	1	1	yes	characteristic
257	C₂×C₇	C₃×#386	1	4	yes	—
258	C₂×C₇	C₃×#390	1	2	yes	—
259	C₂×C₇	C₃×#392	1	4	yes	—
260	C₂×C₇	C₃×#394	1	4	yes	—
261	C₂²×C₃	—	7	1	no	—
262	C₂²×C₃	—	7	2	no	—
263	C₂²×C₃	—	7	4	no	—
264	C₂²×C₃	—	7	4	no	—
265	C₂²×C₃	—	7	4	no	—
266	C₂²×C₃	—	7	4	no	—
267	C₂²×C₃	—	7	8	no	—
268	C₂²×C₃	—	7	4	no	—
269	C₂²×C₃	—	7	2	no	—
270	C₂²×C₃	—	7	2	no	—
271	C₂²×C₃	—	14	8	no	—
272	C₂²×C₃	—	14	16	no	—
273	C₂²×C₃	—	28	8	no	—
274	C₂²×C₃	—	28	8	no	—
275	C₂²×C₃	—	28	16	no	—
276	C₂²×C₃	—	28	16	no	—
277	C₃×C₄	—	14	4	no	—
278	C₃×C₄	—	28	8	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	2	16	no	—
282	C₂³	—	2	8	no	—
283	C₂³	—	2	16	no	—
284	C₂³	—	2	16	no	—
285	C₂³	—	2	8	no	—
286	C₂³	—	4	4	no	—
287	C₂³	—	4	8	no	—
288	C₂³	—	4	8	no	—
289	C₂³	—	4	4	no	—
290	C₂³	—	4	4	no	—
291	C₂³	—	4	4	no	—
292	C₂³	C₂²⋊C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
293	C₂³	C₂²×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
294	C₂³	C₂×D₄×ΓL(1,𝔽₈)	1	4	yes	—
295	C₂³	C₂×D₄×ΓL(1,𝔽₈)	1	2	yes	—
296	C₂³	C₂×D₄×ΓL(1,𝔽₈)	1	4	yes	—
297	C₂³	#41×ΓL(1,𝔽₈)	1	4	yes	—
298	D₄	—	2	32	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	16	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	C₂²⋊C₄×ΓL(1,𝔽₈)	1	4	yes	complemented
307	C₇	C₃×#1438	1	1	yes	characteristic, complemented, Sylow
308	C₂×C₃	—	7	1	no	—
309	C₂×C₃	—	7	4	no	—
310	C₂×C₃	—	7	2	no	—
311	C₂×C₃	—	7	4	no	—
312	C₂×C₃	—	7	4	no	—
313	C₂×C₃	—	28	8	no	—
314	C₂²	—	2	8	no	—
315	C₂²	—	2	16	no	—
316	C₂²	—	4	8	no	—
317	C₂²	—	4	8	no	—
318	C₂²	—	4	16	no	—
319	C₂²	—	4	16	no	—
320	C₂²	C₂×C₂²⋊C₄×ΓL(1,𝔽₈)	1	2	yes	—
321	C₂²	C₂×C₂²⋊C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
322	C₂²	C₄×D₄×ΓL(1,𝔽₈)	1	4	yes	—
323	C₂²	ΓL(1,𝔽₈)×#120	1	4	yes	—
324	C₂²	ΓL(1,𝔽₈)×#120	1	4	yes	—
325	C₂²	ΓL(1,𝔽₈)×#121	1	8	yes	—
326	C₂²	ΓL(1,𝔽₈)×#121	1	4	yes	—
327	C₂²	ΓL(1,𝔽₈)×#123	1	4	yes	—
328	C₂²	ΓL(1,𝔽₈)×#124	1	2	yes	—
329	C₂²	ΓL(1,𝔽₈)×#127	1	2	yes	—
330	C₄	—	2	4	no	—
331	C₄	—	4	8	no	—
332	C₃	—	7	1	no	Sylow
333	C₂	—	4	8	no	—
334	C₂	ΓL(1,𝔽₈)×#379	1	1	yes	characteristic
335	C₂	ΓL(1,𝔽₈)×#386	1	4	yes	—
336	C₂	ΓL(1,𝔽₈)×#390	1	2	yes	—
337	C₂	ΓL(1,𝔽₈)×#392	1	4	yes	—
338	C₂	ΓL(1,𝔽₈)×#394	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×ΓL(1,𝔽₈)
commutator	C₂³×C₇	C₂²×C₃×C₄
Fitting	C₇×#1438	C₃
socle, cosocle	C₂⁴×C₇	C₂³×C₃
prime radical	C₂³×D₄×ΓL(1,𝔽₈)	C₂
hypercenter	#1438	ΓL(1,𝔽₈)
hypocenter	C₇	C₃×#1438
LCS	G ▷ C₂³×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ #1438

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂²⋊C₄×ΓL(1,𝔽₈)	C₂	semidirect
3. C₂×ΓL(1,𝔽₈)×#95	C₂	semidirect
4. C₇×#1438	C₃	semidirect
8. C₂²×D₄×ΓL(1,𝔽₈)	C₄	semidirect
15. C₂²×C₇×C₂²⋊C₄	C₂×C₃	semidirect
16. C₂×C₇×#95	C₂×C₃	semidirect
35. C₂²×C₄×ΓL(1,𝔽₈)	D₄	semidirect
40. C₂²×C₇×D₄	C₃×C₄	semidirect
62. C₂³×ΓL(1,𝔽₈)	C₂²⋊C₄	semidirect
76. C₂×C₄×ΓL(1,𝔽₈)	C₂²⋊C₄	semidirect
77. #1438	ΓL(1,𝔽₈)	direct (N × H)
95. C₂²×C₄×C₇	C₃×D₄	semidirect
125. C₂²×C₂²⋊C₄	C₂×ΓL(1,𝔽₈)	semidirect
126. C₂×#95	C₂×ΓL(1,𝔽₈)	semidirect
140. C₂³×C₇	C₃×C₂²⋊C₄	semidirect
154. C₂×C₄×C₇	C₃×C₂²⋊C₄	semidirect
183. C₂²×D₄	C₄×ΓL(1,𝔽₈)	semidirect
235. ΓL(1,𝔽₈)	#1438	direct (N × H)
253. C₂²×C₄	D₄×ΓL(1,𝔽₈)	semidirect
292. C₂³	C₂²⋊C₄×ΓL(1,𝔽₈)	semidirect
306. C₂×C₄	C₂²⋊C₄×ΓL(1,𝔽₈)	semidirect
307. C₇	C₃×#1438	semidirect

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
C₂²×C₂²⋊C₄×ΓL(1,𝔽₈)	2
C₂×ΓL(1,𝔽₈)×#95	2
C₇×#1438	3
C₃×#1438	7

Subgroups — ΓL(1,𝔽8)×#1438 #72230200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ΓL(1,𝔽₈)×#1438 #72230200