Subgroups — #90465⋊C₃ #13057508

Order 1344.

536 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10621518	C₂	1	1	yes	maximal, characteristic, complemented
2	#6548⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	#6513⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#1141⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#6479⋊C₃	C₂	1	2	yes	maximal, complemented
7	#6477⋊C₃	C₂	1	2	yes	maximal, complemented
8	#6474⋊C₃	C₂	1	2	yes	maximal, complemented
9	D₈×AGL(1,𝔽₇)	C₂	1	2	yes	maximal, complemented
10	#6471⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#6470⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#90465	C₃	1	1	yes	maximal, characteristic, complemented, Hall
13	#41×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
14	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
15	C₂×(C₂²⋊D₇)⋊C₃	—	2	2	no	—
16	#66659	C₂²	1	2	yes	complemented
17	#1159⋊C₃	—	2	1	no	—
18	#1159⋊C₃	C₂²	1	2	yes	complemented
19	D₄×AGL(1,𝔽₇)	—	2	2	no	—
20	D₄×AGL(1,𝔽₇)	—	2	1	no	—
21	D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
22	D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
23	#1157⋊C₃	—	2	1	no	—
24	#1157⋊C₃	C₂²	1	1	yes	characteristic
25	#1157⋊C₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄⋊AGL(1,𝔽₇)	—	2	1	no	—
27	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
28	SD₁₆×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
29	D₈×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
30	M₁₆×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
31	#1144⋊C₃	C₂²	1	1	yes	characteristic, complemented
32	#1143⋊C₃	C₂²	1	1	yes	characteristic, complemented
33	#1142⋊C₃	C₂²	1	1	yes	characteristic, complemented
34	#1141⋊C₃	C₂²	1	1	yes	characteristic, complemented
35	#1141⋊C₃	C₂²	1	2	yes	complemented
36	#1141⋊C₃	C₂²	1	2	yes	complemented
37	C₂×ΓL(1,𝔽₈)⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	D₅₆⋊C₃	C₂²	1	2	yes	complemented
39	#1132⋊C₃	C₂²	1	2	yes	complemented
40	#1131⋊C₃	C₂²	1	2	yes	complemented
41	C₈×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
42	#6553	C₂×C₃	1	1	yes	characteristic, complemented
43	#6548	C₂×C₃	1	1	yes	characteristic, complemented
44	C₇×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
45	#6513	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#1141	C₂×C₃	1	1	yes	characteristic, complemented
47	#6479	C₂×C₃	1	2	yes	complemented
48	#6477	C₂×C₃	1	2	yes	complemented
49	#6474	C₂×C₃	1	2	yes	complemented
50	D₇×D₈	C₂×C₃	1	2	yes	complemented
51	#6471	C₂×C₃	1	1	yes	characteristic, complemented
52	#6470	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃×#576	—	7	1	no	maximal, Hall
54	C₂³×ΓL(1,𝔽₈)	—	2	1	no	—
55	C₂²×AGL(1,𝔽₇)	—	2	1	no	—
56	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
57	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
58	Q₈×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
59	D₄×ΓL(1,𝔽₈)	—	2	1	no	—
60	D₄×ΓL(1,𝔽₈)	—	2	1	no	—
61	D₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
62	D₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
63	C₂×C₄×ΓL(1,𝔽₈)	—	2	1	no	—
64	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
65	(C₂²⋊D₇)⋊C₃	—	2	1	no	—
66	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
67	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
68	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
69	(C₂²⋊D₇)⋊C₃	D₄	1	2	yes	—
70	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
71	C₄⋊AGL(1,𝔽₇)	—	2	2	no	—
72	C₄⋊AGL(1,𝔽₇)	—	2	1	no	—
73	C₄⋊AGL(1,𝔽₇)	D₄	1	1	yes	characteristic
74	C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	—
75	C₄⋊AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
76	C₄×AGL(1,𝔽₇)	—	2	1	no	—
77	C₄×AGL(1,𝔽₇)	—	2	2	no	—
78	C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	—
79	ΓL(1,𝔽₈)⋊Q₈	D₄	1	1	yes	characteristic
80	ΓL(1,𝔽₈)⋊Q₈	C₂³	1	1	yes	characteristic
81	C₈×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
82	ΓL(1,𝔽₈)⋊C₈	C₂³	1	1	yes	characteristic
83	ΓL(1,𝔽₈)⋊C₈	C₂³	1	1	yes	characteristic
84	C₇×#41	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊D₇	—	2	2	no	—
87	#1161	C₂²×C₃	1	2	yes	complemented
88	#1159	—	2	1	no	—
89	#1159	C₂²×C₃	1	2	yes	complemented
90	D₄×D₇	—	2	2	no	—
91	D₄×D₇	—	2	1	no	—
92	D₄×D₇	C₂²×C₃	1	2	yes	complemented
93	D₄×D₇	C₂²×C₃	1	2	yes	complemented
94	#1157	—	2	1	no	—
95	#1157	C₂²×C₃	1	1	yes	characteristic
96	#1157	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₂×D₂₈	—	2	1	no	—
98	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₇×SD₁₆	C₂²×C₃	1	2	yes	complemented
100	C₇×D₈	C₂²×C₃	1	2	yes	complemented
101	C₇×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
102	#1144	C₂²×C₃	1	1	yes	characteristic, complemented
103	#1143	C₂²×C₃	1	1	yes	characteristic, complemented
104	#1142	C₂²×C₃	1	1	yes	characteristic, complemented
105	#1141	C₂²×C₃	1	1	yes	characteristic, complemented
106	#1141	C₂²×C₃	1	2	yes	complemented
107	#1141	C₂²×C₃	1	2	yes	complemented
108	C₂×C₇⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
109	D₅₆	C₂²×C₃	1	2	yes	complemented
110	#1132	C₂²×C₃	1	2	yes	complemented
111	#1131	C₂²×C₃	1	2	yes	complemented
112	C₈×D₇	C₂²×C₃	1	2	yes	complemented
113	C₃×H(5,𝔽₂)	—	7	1	no	—
114	C₃×H(5,𝔽₂)	—	7	1	no	—
115	C₃×AGL(1,ℤ/8)	—	7	1	no	—
116	C₃×AGL(1,ℤ/8)	—	7	2	no	—
117	C₃×AGL(1,ℤ/8)	—	7	2	no	—
118	C₃×AGL(1,ℤ/8)	—	7	1	no	—
119	C₃×#135	—	7	2	no	—
120	C₃×#135	—	7	1	no	—
121	C₂×C₃×D₈	—	7	2	no	—
122	C₂×C₃×D₈	—	7	1	no	—
123	C₃×#131	—	7	1	no	—
124	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
125	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
126	C₂²×ΓL(1,𝔽₈)	—	8	1	no	—
127	C₂²×ΓL(1,𝔽₈)	C₂×D₄	1	1	yes	characteristic
128	C₂×AGL(1,𝔽₇)	—	2	2	no	—
129	C₂×AGL(1,𝔽₇)	—	2	1	no	—
130	C₂×AGL(1,𝔽₇)	—	8	2	no	—
131	C₂×AGL(1,𝔽₇)	—	8	2	no	—
132	C₂×AGL(1,𝔽₇)	—	8	1	no	—
133	C₂×AGL(1,𝔽₇)	C₂×D₄	1	2	yes	—
134	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
135	C₄×ΓL(1,𝔽₈)	C₂×D₄	1	1	yes	characteristic
136	C₄×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
137	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
138	ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	2	yes	—
139	#576	—	7	1	no	Sylow
140	C₂³×C₇	—	2	1	no	—
141	C₂²×D₇	—	2	1	no	—
142	C₂²×D₇	—	2	2	no	—
143	C₂²×D₇	—	2	2	no	—
144	C₇×Q₈	C₂³×C₃	1	1	yes	characteristic
145	C₇×D₄	—	2	1	no	—
146	C₇×D₄	—	2	1	no	—
147	C₇×D₄	C₂³×C₃	1	2	yes	—
148	C₇×D₄	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₄×C₇	—	2	1	no	—
150	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
151	C₂²⋊D₇	—	2	1	no	—
152	C₂²⋊D₇	—	2	2	no	—
153	C₂²⋊D₇	—	2	2	no	—
154	C₂²⋊D₇	—	2	2	no	—
155	C₂²⋊D₇	C₃×D₄	1	2	yes	—
156	C₂×Dic₇	—	2	2	no	—
157	D₂₈	—	2	2	no	—
158	D₂₈	—	2	1	no	—
159	D₂₈	C₃×D₄	1	1	yes	characteristic
160	D₂₈	C₂³×C₃	1	2	yes	—
161	D₂₈	C₂³×C₃	1	1	yes	characteristic
162	C₄×D₇	—	2	1	no	—
163	C₄×D₇	—	2	2	no	—
164	C₄×D₇	C₂³×C₃	1	2	yes	—
165	Dic₁₄	C₃×D₄	1	1	yes	characteristic
166	Dic₁₄	C₂³×C₃	1	1	yes	characteristic
167	C₇×C₈	C₂³×C₃	1	2	yes	—
168	C₇⋊C₈	C₂³×C₃	1	1	yes	characteristic
169	C₇⋊C₈	C₂³×C₃	1	1	yes	characteristic
170	C₃×#41	—	7	1	no	—
171	C₃×#41	—	7	1	no	—
172	C₃×#41	—	7	2	no	—
173	C₃×#41	—	7	2	no	—
174	C₃×#41	—	7	1	no	—
175	C₃×#41	—	14	1	no	—
176	C₃×#41	—	14	1	no	—
177	C₂×C₃×D₄	—	7	1	no	—
178	C₂×C₃×D₄	—	7	2	no	—
179	C₂×C₃×D₄	—	7	2	no	—
180	C₂×C₃×D₄	—	7	1	no	—
181	C₂×C₃×D₄	—	14	1	no	—
182	C₂×C₃×D₄	—	14	1	no	—
183	C₂×C₃×D₄	—	14	2	no	—
184	C₂×C₃×D₄	—	14	2	no	—
185	C₃×Q₁₆	—	7	1	no	—
186	C₃×SD₁₆	—	7	2	no	—
187	C₃×SD₁₆	—	7	1	no	—
188	C₃×SD₁₆	—	7	1	no	—
189	C₃×SD₁₆	—	7	2	no	—
190	C₃×D₈	—	7	1	no	—
191	C₃×D₈	—	7	2	no	—
192	C₃×D₈	—	7	2	no	—
193	C₃×D₈	—	7	2	no	—
194	C₃×D₈	—	7	2	no	—
195	C₃×M₁₆	—	7	2	no	—
196	C₃×M₁₆	—	7	1	no	—
197	C₂×C₃×C₈	—	7	2	no	—
198	C₂×C₃×C₈	—	7	1	no	—
199	C₂×ΓL(1,𝔽₈)	—	2	1	no	—
200	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
201	C₂×ΓL(1,𝔽₈)	—	4	2	no	—
202	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
203	AGL(1,𝔽₇)	—	2	2	no	—
204	AGL(1,𝔽₇)	—	4	2	no	—
205	AGL(1,𝔽₇)	—	4	1	no	—
206	H(5,𝔽₂)	—	7	1	no	—
207	H(5,𝔽₂)	—	7	1	no	—
208	AGL(1,ℤ/8)	—	7	2	no	—
209	AGL(1,ℤ/8)	—	7	2	no	—
210	AGL(1,ℤ/8)	—	7	1	no	—
211	AGL(1,ℤ/8)	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
212	#135	—	7	1	no	—
213	#135	—	7	2	no	—
214	C₂×D₈	—	7	1	no	—
215	C₂×D₈	—	7	2	no	—
216	#131	—	7	1	no	—
217	C₂²×C₇	—	2	2	no	—
218	C₂²×C₇	—	2	1	no	—
219	C₂²×C₇	—	8	1	no	—
220	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
221	C₂×D₇	—	2	2	no	—
222	C₂×D₇	—	2	1	no	—
223	C₂×D₇	—	8	2	no	—
224	C₂×D₇	—	8	2	no	—
225	C₂×D₇	—	8	1	no	—
226	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
227	C₄×C₇	—	2	1	no	—
228	C₄×C₇	C₂×C₃×D₄	1	1	yes	characteristic
229	C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
230	Dic₇	—	2	1	no	—
231	Dic₇	C₂×C₃×D₄	1	2	yes	—
232	C₂³×C₃	—	14	1	no	—
233	C₂³×C₃	—	14	2	no	—
234	C₂³×C₃	—	14	2	no	—
235	C₂³×C₃	—	14	1	no	—
236	C₃×Q₈	—	7	1	no	—
237	C₃×Q₈	—	7	1	no	—
238	C₃×Q₈	—	7	1	no	—
239	C₃×D₄	—	7	1	no	—
240	C₃×D₄	—	7	2	no	—
241	C₃×D₄	—	7	2	no	—
242	C₃×D₄	—	7	1	no	—
243	C₃×D₄	—	7	2	no	—
244	C₃×D₄	—	7	1	no	—
245	C₃×D₄	—	14	1	no	—
246	C₃×D₄	—	14	1	no	—
247	C₃×D₄	—	14	1	no	—
248	C₃×D₄	—	14	2	no	—
249	C₃×D₄	—	14	2	no	—
250	C₃×D₄	—	14	2	no	—
251	C₃×D₄	—	14	2	no	—
252	C₃×D₄	—	14	1	no	—
253	C₂×C₃×C₄	—	7	2	no	—
254	C₂×C₃×C₄	—	7	1	no	—
255	C₂×C₃×C₄	—	14	1	no	—
256	C₂×C₃×C₄	—	14	2	no	—
257	C₂×C₃×C₄	—	14	1	no	—
258	C₂×C₃×C₄	—	14	2	no	—
259	C₃×C₈	—	7	1	no	—
260	C₃×C₈	—	7	1	no	—
261	C₃×C₈	—	7	2	no	—
262	ΓL(1,𝔽₈)	#576	1	1	yes	characteristic, complemented, Hall
263	#41	—	7	1	no	—
264	#41	—	7	2	no	—
265	#41	—	7	2	no	—
266	#41	—	7	1	no	—
267	#41	—	14	1	no	—
268	#41	—	14	1	no	—
269	#41	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
270	C₂×D₄	—	7	2	no	—
271	C₂×D₄	—	7	2	no	—
272	C₂×D₄	—	7	1	no	—
273	C₂×D₄	—	14	1	no	—
274	C₂×D₄	—	14	2	no	—
275	C₂×D₄	—	14	1	no	—
276	C₂×D₄	—	14	2	no	—
277	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
278	Q₁₆	—	7	1	no	—
279	SD₁₆	—	7	1	no	—
280	SD₁₆	—	7	1	no	—
281	SD₁₆	—	7	2	no	—
282	SD₁₆	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
283	D₈	—	7	2	no	—
284	D₈	—	7	1	no	—
285	D₈	—	7	2	no	—
286	D₈	—	7	2	no	—
287	D₈	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
288	M₁₆	—	7	2	no	—
289	M₁₆	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
290	C₂×C₈	—	7	1	no	—
291	C₂×C₈	—	7	2	no	—
292	C₂×C₇	—	2	1	no	—
293	C₂×C₇	—	4	1	no	—
294	C₂×C₇	—	4	2	no	—
295	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
296	D₇	—	2	2	no	—
297	D₇	—	4	2	no	—
298	D₇	—	4	1	no	—
299	C₂²×C₃	—	7	2	no	—
300	C₂²×C₃	—	7	1	no	—
301	C₂²×C₃	—	14	1	no	—
302	C₂²×C₃	—	14	2	no	—
303	C₂²×C₃	—	14	2	no	—
304	C₂²×C₃	—	14	1	no	—
305	C₂²×C₃	—	56	1	no	—
306	C₂²×C₃	—	56	1	no	—
307	C₂²×C₃	—	56	2	no	—
308	C₂²×C₃	—	56	2	no	—
309	C₃×C₄	—	7	2	no	—
310	C₃×C₄	—	7	1	no	—
311	C₃×C₄	—	7	1	no	—
312	C₃×C₄	—	14	1	no	—
313	C₃×C₄	—	14	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	14	2	no	—
316	C₂³	—	14	2	no	—
317	C₂³	—	14	1	no	—
318	Q₈	—	7	1	no	—
319	Q₈	—	7	1	no	—
320	Q₈	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
321	D₄	—	2	1	no	—
322	D₄	—	2	1	no	—
323	D₄	—	7	2	no	—
324	D₄	—	7	1	no	—
325	D₄	—	7	2	no	—
326	D₄	—	7	1	no	—
327	D₄	—	14	2	no	—
328	D₄	—	14	2	no	—
329	D₄	—	14	2	no	—
330	D₄	—	14	2	no	—
331	D₄	—	14	1	no	—
332	D₄	—	14	1	no	—
333	D₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
334	D₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	7	2	no	—
337	C₂×C₄	—	14	2	no	—
338	C₂×C₄	—	14	2	no	—
339	C₂×C₄	—	14	1	no	—
340	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
341	C₈	—	7	1	no	—
342	C₈	—	7	1	no	—
343	C₈	C₂²×AGL(1,𝔽₇)	1	2	yes	—
344	C₇	C₃×#576	1	1	yes	characteristic, complemented, Sylow
345	C₂×C₃	—	7	1	no	—
346	C₂×C₃	—	14	1	no	—
347	C₂×C₃	—	14	2	no	—
348	C₂×C₃	—	28	2	no	—
349	C₂×C₃	—	28	1	no	—
350	C₂×C₃	—	28	2	no	—
351	C₂×C₃	—	28	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	7	2	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	14	2	no	—
357	C₂²	—	14	1	no	—
358	C₂²	—	56	1	no	—
359	C₂²	—	56	2	no	—
360	C₂²	—	56	2	no	—
361	C₂²	D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	7	2	no	—
364	C₄	—	14	1	no	—
365	C₄	D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
366	C₄	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
367	C₃	—	7	1	no	Sylow
368	C₂	—	2	1	no	—
369	C₂	—	4	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	14	2	no	—
372	C₂	—	28	2	no	—
373	C₂	—	28	1	no	—
374	C₂	C₂×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×AGL(1,𝔽₇)
commutator, cosocle	C₄×C₇	C₂⁴×C₃
Frattini	C₄	C₂³×AGL(1,𝔽₇)
Fitting	C₇×AGL(1,ℤ/8)	C₂×C₃
socle	C₂×C₇	C₂²×C₃×D₄
hypercenter	AGL(1,ℤ/8)	AGL(1,𝔽₇)
hypocenter	C₇	C₃×#576
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #10621518	C₂	semidirect
2. #6548⋊C₃	C₂	semidirect
3. ΓL(1,𝔽₈)×AGL(1,ℤ/8)	C₂	semidirect
4. #6513⋊C₃	C₂	semidirect
5. C₂×#1141⋊C₃	C₂	semidirect
6. #6479⋊C₃	C₂	semidirect
7. #6477⋊C₃	C₂	semidirect
8. #6474⋊C₃	C₂	semidirect
9. D₈×AGL(1,𝔽₇)	C₂	semidirect
10. #6471⋊C₃	C₂	semidirect
11. #6470⋊C₃	C₂	semidirect
12. #90465	C₃	semidirect
13. #41×ΓL(1,𝔽₈)	C₂²	semidirect
14. C₂×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
16. #66659	C₂²	semidirect
18. #1159⋊C₃	C₂²	semidirect
21. D₄×AGL(1,𝔽₇)	C₂²	semidirect
22. D₄×AGL(1,𝔽₇)	C₂²	semidirect
25. #1157⋊C₃	C₂²	semidirect
27. C₂×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
28. SD₁₆×ΓL(1,𝔽₈)	C₂²	semidirect
29. D₈×ΓL(1,𝔽₈)	C₂²	semidirect
30. M₁₆×ΓL(1,𝔽₈)	C₂²	semidirect
31. #1144⋊C₃	C₂²	semidirect
32. #1143⋊C₃	C₂²	semidirect
33. #1142⋊C₃	C₂²	semidirect
34. #1141⋊C₃	C₂²	semidirect
35. #1141⋊C₃	C₂²	semidirect
36. #1141⋊C₃	C₂²	semidirect
37. C₂×ΓL(1,𝔽₈)⋊C₈	C₂²	semidirect
38. D₅₆⋊C₃	C₂²	semidirect
39. #1132⋊C₃	C₂²	semidirect
40. #1131⋊C₃	C₂²	semidirect
41. C₈×AGL(1,𝔽₇)	C₂²	semidirect
42. #6553	C₂×C₃	semidirect
43. #6548	C₂×C₃	semidirect
44. C₇×AGL(1,ℤ/8)	C₂×C₃	semidirect
45. #6513	C₂×C₃	semidirect
46. C₂×#1141	C₂×C₃	semidirect
47. #6479	C₂×C₃	semidirect
48. #6477	C₂×C₃	semidirect
49. #6474	C₂×C₃	semidirect
50. D₇×D₈	C₂×C₃	semidirect
51. #6471	C₂×C₃	semidirect
52. #6470	C₂×C₃	semidirect
84. C₇×#41	C₂²×C₃	semidirect
85. C₂×C₇×D₄	C₂²×C₃	semidirect
87. #1161	C₂²×C₃	semidirect
89. #1159	C₂²×C₃	semidirect
92. D₄×D₇	C₂²×C₃	semidirect
93. D₄×D₇	C₂²×C₃	semidirect
96. #1157	C₂²×C₃	semidirect
98. C₂×D₂₈	C₂²×C₃	semidirect
99. C₇×SD₁₆	C₂²×C₃	semidirect
100. C₇×D₈	C₂²×C₃	semidirect
101. C₇×M₁₆	C₂²×C₃	semidirect
102. #1144	C₂²×C₃	semidirect
103. #1143	C₂²×C₃	semidirect
104. #1142	C₂²×C₃	semidirect
105. #1141	C₂²×C₃	semidirect
106. #1141	C₂²×C₃	semidirect
107. #1141	C₂²×C₃	semidirect
108. C₂×C₇⋊C₈	C₂²×C₃	semidirect
109. D₅₆	C₂²×C₃	semidirect
110. #1132	C₂²×C₃	semidirect
111. #1131	C₂²×C₃	semidirect
112. C₈×D₇	C₂²×C₃	semidirect
211. AGL(1,ℤ/8)	AGL(1,𝔽₇)	semidirect
262. ΓL(1,𝔽₈)	#576	semidirect
269. #41	C₂×AGL(1,𝔽₇)	semidirect
277. C₂×D₄	C₂×AGL(1,𝔽₇)	semidirect
282. SD₁₆	C₂×AGL(1,𝔽₇)	semidirect
287. D₈	C₂×AGL(1,𝔽₇)	semidirect
289. M₁₆	C₂×AGL(1,𝔽₇)	semidirect
344. C₇	C₃×#576	semidirect

Maximal subgroups

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

subgroup	index
#10621518	2
#6548⋊C₃	2
ΓL(1,𝔽₈)×AGL(1,ℤ/8)	2
#6513⋊C₃	2
C₂×#1141⋊C₃	2
#6479⋊C₃	2
#6477⋊C₃	2
#6474⋊C₃	2
D₈×AGL(1,𝔽₇)	2
#6471⋊C₃	2
#6470⋊C₃	2
#90465	3
C₃×#576	7

Subgroups — #90465⋊C3 #13057508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #90465⋊C₃ #13057508