Subgroups — #90466⋊C₃ #13057509

Order 1344.

516 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10621519	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×#1142⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#6478⋊C₃	C₂	1	2	yes	maximal, complemented
7	SD₁₆×AGL(1,𝔽₇)	C₂	1	2	yes	maximal, complemented
8	#6475⋊C₃	C₂	1	2	yes	maximal, complemented
9	#6474⋊C₃	C₂	1	2	yes	maximal, complemented
10	#6472⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#6470⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#90466	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
15	C₂×(C₂²⋊D₇)⋊C₃	—	2	2	no	—
16	Q₈×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
17	#1159⋊C₃	—	2	2	no	—
18	#1159⋊C₃	—	2	1	no	—
19	#1159⋊C₃	C₂²	1	2	yes	—
20	#1159⋊C₃	C₂²	1	2	yes	complemented
21	D₄×AGL(1,𝔽₇)	—	2	1	no	—
22	D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	—
23	#1157⋊C₃	—	2	1	no	—
24	#1157⋊C₃	C₂²	1	1	yes	characteristic
25	#1157⋊C₃	C₂²	1	1	yes	characteristic
26	C₂×ΓL(1,𝔽₈)⋊Q₈	—	2	1	no	—
27	C₂×ΓL(1,𝔽₈)⋊Q₈	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	2	yes	complemented
34	#1142⋊C₃	C₂²	1	1	yes	characteristic, complemented
35	#1142⋊C₃	C₂²	1	2	yes	complemented
36	#1141⋊C₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×ΓL(1,𝔽₈)⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	Dic₂₈⋊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	#6554	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×#1142	C₂×C₃	1	1	yes	characteristic, complemented
47	#6478	C₂×C₃	1	2	yes	complemented
48	D₇×SD₁₆	C₂×C₃	1	2	yes	complemented
49	#6475	C₂×C₃	1	2	yes	complemented
50	#6474	C₂×C₃	1	2	yes	complemented
51	#6472	C₂×C₃	1	1	yes	characteristic, complemented
52	#6470	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃×#577	—	7	1	no	maximal, Hall
54	C₂³×ΓL(1,𝔽₈)	—	2	1	no	—
55	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
56	Q₈×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
57	D₄×ΓL(1,𝔽₈)	—	2	1	no	—
58	D₄×ΓL(1,𝔽₈)	—	2	1	no	—
59	D₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
60	D₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
61	C₂×C₄×ΓL(1,𝔽₈)	—	2	1	no	—
62	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
63	(C₂²⋊D₇)⋊C₃	—	2	1	no	—
64	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
65	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
66	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
67	(C₂²⋊D₇)⋊C₃	D₄	1	2	yes	—
68	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
69	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
70	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
71	C₄⋊AGL(1,𝔽₇)	D₄	1	1	yes	characteristic
72	C₄⋊AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
73	C₄×AGL(1,𝔽₇)	—	2	2	no	—
74	C₄×AGL(1,𝔽₇)	—	2	1	no	—
75	C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	—
76	ΓL(1,𝔽₈)⋊Q₈	—	2	1	no	—
77	ΓL(1,𝔽₈)⋊Q₈	—	2	2	no	—
78	ΓL(1,𝔽₈)⋊Q₈	D₄	1	1	yes	characteristic
79	ΓL(1,𝔽₈)⋊Q₈	C₂³	1	2	yes	—
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
86	C₂×C₂²⋊D₇	—	2	2	no	—
87	Q₈×D₇	C₂²×C₃	1	2	yes	complemented
88	#1159	—	2	2	no	—
89	#1159	—	2	1	no	—
90	#1159	C₂²×C₃	1	2	yes	—
91	#1159	C₂²×C₃	1	2	yes	complemented
92	D₄×D₇	—	2	1	no	—
93	D₄×D₇	C₂²×C₃	1	2	yes	—
94	#1157	—	2	1	no	—
95	#1157	C₂²×C₃	1	1	yes	characteristic
96	#1157	C₂²×C₃	1	1	yes	characteristic
97	C₂×Dic₁₄	—	2	1	no	—
98	C₂×Dic₁₄	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	2	yes	complemented
105	#1142	C₂²×C₃	1	1	yes	characteristic, complemented
106	#1142	C₂²×C₃	1	2	yes	complemented
107	#1141	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂×C₇⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
109	Dic₂₈	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	C₃×2₋¹⁺⁴	—	7	1	no	—
114	C₃×H(5,𝔽₂)	—	7	1	no	—
115	C₃×#137	—	7	1	no	—
116	C₃×#137	—	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×SD₁₆	—	7	2	no	—
122	C₂×C₃×SD₁₆	—	7	1	no	—
123	C₃×#131	—	7	1	no	—
124	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
125	C₂²×ΓL(1,𝔽₈)	—	2	2	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	1	no	—
129	C₂×AGL(1,𝔽₇)	—	8	2	no	—
130	C₂×AGL(1,𝔽₇)	C₂×D₄	1	2	yes	—
131	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
132	C₄×ΓL(1,𝔽₈)	C₂×D₄	1	1	yes	characteristic
133	C₄×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
134	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
135	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
136	ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	2	yes	—
137	#577	—	7	1	no	Sylow
138	C₂³×C₇	—	2	1	no	—
139	C₂²×D₇	—	2	2	no	—
140	C₇×Q₈	C₂³×C₃	1	1	yes	characteristic
141	C₇×D₄	—	2	1	no	—
142	C₇×D₄	—	2	1	no	—
143	C₇×D₄	C₂³×C₃	1	1	yes	characteristic
144	C₇×D₄	C₂³×C₃	1	2	yes	—
145	C₂×C₄×C₇	—	2	1	no	—
146	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
147	C₂²⋊D₇	—	2	1	no	—
148	C₂²⋊D₇	—	2	2	no	—
149	C₂²⋊D₇	—	2	2	no	—
150	C₂²⋊D₇	—	2	2	no	—
151	C₂²⋊D₇	C₃×D₄	1	2	yes	—
152	C₂×Dic₇	—	2	1	no	—
153	C₂×Dic₇	—	2	2	no	—
154	C₂×Dic₇	—	2	2	no	—
155	D₂₈	C₃×D₄	1	1	yes	characteristic
156	D₂₈	C₂³×C₃	1	1	yes	characteristic
157	C₄×D₇	—	2	2	no	—
158	C₄×D₇	—	2	1	no	—
159	C₄×D₇	C₂³×C₃	1	2	yes	—
160	Dic₁₄	—	2	1	no	—
161	Dic₁₄	—	2	2	no	—
162	Dic₁₄	C₃×D₄	1	1	yes	characteristic
163	Dic₁₄	C₂³×C₃	1	2	yes	—
164	Dic₁₄	C₂³×C₃	1	1	yes	characteristic
165	C₇×C₈	C₂³×C₃	1	2	yes	—
166	C₇⋊C₈	C₂³×C₃	1	1	yes	characteristic
167	C₇⋊C₈	C₂³×C₃	1	1	yes	characteristic
168	C₃×#41	—	7	1	no	—
169	C₃×#41	—	7	1	no	—
170	C₃×#41	—	7	2	no	—
171	C₃×#41	—	7	2	no	—
172	C₃×#41	—	7	1	no	—
173	C₃×#41	—	14	1	no	—
174	C₃×#41	—	14	2	no	—
175	C₃×#41	—	14	1	no	—
176	C₂×C₃×Q₈	—	7	1	no	—
177	C₂×C₃×Q₈	—	7	2	no	—
178	C₂×C₃×Q₈	—	14	1	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	2	no	—
183	C₃×Q₁₆	—	7	2	no	—
184	C₃×Q₁₆	—	7	1	no	—
185	C₃×SD₁₆	—	7	2	no	—
186	C₃×SD₁₆	—	7	1	no	—
187	C₃×SD₁₆	—	7	2	no	—
188	C₃×SD₁₆	—	7	2	no	—
189	C₃×SD₁₆	—	7	1	no	—
190	C₃×SD₁₆	—	7	2	no	—
191	C₃×D₈	—	7	1	no	—
192	C₃×D₈	—	7	2	no	—
193	C₃×M₁₆	—	7	2	no	—
194	C₃×M₁₆	—	7	1	no	—
195	C₂×C₃×C₈	—	7	2	no	—
196	C₂×C₃×C₈	—	7	1	no	—
197	C₂×ΓL(1,𝔽₈)	—	2	1	no	—
198	C₂×ΓL(1,𝔽₈)	—	4	2	no	—
199	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
200	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
201	AGL(1,𝔽₇)	—	2	2	no	—
202	AGL(1,𝔽₇)	—	4	1	no	—
203	2₋¹⁺⁴	—	7	1	no	—
204	H(5,𝔽₂)	—	7	1	no	—
205	#137	—	7	2	no	—
206	#137	—	7	1	no	—
207	AGL(1,ℤ/8)	—	7	2	no	—
208	AGL(1,ℤ/8)	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
209	#135	—	7	1	no	—
210	#135	—	7	2	no	—
211	C₂×SD₁₆	—	7	1	no	—
212	C₂×SD₁₆	—	7	2	no	—
213	#131	—	7	1	no	—
214	C₂²×C₇	—	2	1	no	—
215	C₂²×C₇	—	2	2	no	—
216	C₂²×C₇	—	8	1	no	—
217	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
218	C₂×D₇	—	2	1	no	—
219	C₂×D₇	—	8	2	no	—
220	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
221	C₄×C₇	—	2	1	no	—
222	C₄×C₇	C₂×C₃×D₄	1	1	yes	characteristic
223	C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
224	Dic₇	—	2	2	no	—
225	Dic₇	—	2	1	no	—
226	Dic₇	C₂×C₃×D₄	1	2	yes	—
227	C₂³×C₃	—	14	1	no	—
228	C₂³×C₃	—	14	2	no	—
229	C₃×Q₈	—	7	1	no	—
230	C₃×Q₈	—	7	2	no	—
231	C₃×Q₈	—	7	1	no	—
232	C₃×Q₈	—	7	1	no	—
233	C₃×Q₈	—	14	2	no	—
234	C₃×Q₈	—	14	1	no	—
235	C₃×D₄	—	7	1	no	—
236	C₃×D₄	—	7	2	no	—
237	C₃×D₄	—	7	1	no	—
238	C₃×D₄	—	7	1	no	—
239	C₃×D₄	—	7	2	no	—
240	C₃×D₄	—	14	1	no	—
241	C₃×D₄	—	14	1	no	—
242	C₃×D₄	—	14	2	no	—
243	C₃×D₄	—	14	2	no	—
244	C₃×D₄	—	14	1	no	—
245	C₃×D₄	—	14	2	no	—
246	C₂×C₃×C₄	—	7	2	no	—
247	C₂×C₃×C₄	—	7	1	no	—
248	C₂×C₃×C₄	—	14	1	no	—
249	C₂×C₃×C₄	—	14	1	no	—
250	C₂×C₃×C₄	—	14	2	no	—
251	C₂×C₃×C₄	—	14	2	no	—
252	C₂×C₃×C₄	—	14	2	no	—
253	C₂×C₃×C₄	—	14	1	no	—
254	C₃×C₈	—	7	1	no	—
255	C₃×C₈	—	7	1	no	—
256	C₃×C₈	—	7	2	no	—
257	ΓL(1,𝔽₈)	#577	1	1	yes	characteristic, complemented, Hall
258	#41	—	7	1	no	—
259	#41	—	7	2	no	—
260	#41	—	7	2	no	—
261	#41	—	7	1	no	—
262	#41	—	14	1	no	—
263	#41	—	14	2	no	—
264	#41	—	14	1	no	—
265	#41	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
266	C₂×Q₈	—	7	2	no	—
267	C₂×Q₈	—	7	1	no	—
268	C₂×Q₈	—	14	1	no	—
269	C₂×D₄	—	7	2	no	—
270	C₂×D₄	—	14	1	no	—
271	C₂×D₄	—	14	2	no	—
272	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
273	Q₁₆	—	7	1	no	—
274	Q₁₆	—	7	2	no	—
275	SD₁₆	—	7	1	no	—
276	SD₁₆	—	7	2	no	—
277	SD₁₆	—	7	2	no	—
278	SD₁₆	—	7	1	no	—
279	SD₁₆	—	7	2	no	—
280	SD₁₆	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
281	D₈	—	7	1	no	—
282	D₈	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
283	M₁₆	—	7	2	no	—
284	M₁₆	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
285	C₂×C₈	—	7	1	no	—
286	C₂×C₈	—	7	2	no	—
287	C₂×C₇	—	2	1	no	—
288	C₂×C₇	—	4	2	no	—
289	C₂×C₇	—	4	1	no	—
290	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
291	D₇	—	2	2	no	—
292	D₇	—	4	1	no	—
293	C₂²×C₃	—	7	2	no	—
294	C₂²×C₃	—	7	1	no	—
295	C₂²×C₃	—	14	1	no	—
296	C₂²×C₃	—	14	2	no	—
297	C₂²×C₃	—	14	1	no	—
298	C₂²×C₃	—	56	1	no	—
299	C₂²×C₃	—	56	2	no	—
300	C₃×C₄	—	7	2	no	—
301	C₃×C₄	—	7	1	no	—
302	C₃×C₄	—	7	1	no	—
303	C₃×C₄	—	14	1	no	—
304	C₃×C₄	—	14	1	no	—
305	C₃×C₄	—	14	2	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	14	2	no	—
308	Q₈	—	7	1	no	—
309	Q₈	—	7	2	no	—
310	Q₈	—	7	1	no	—
311	Q₈	—	14	2	no	—
312	Q₈	—	14	1	no	—
313	Q₈	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
314	D₄	—	2	1	no	—
315	D₄	—	2	1	no	—
316	D₄	—	7	2	no	—
317	D₄	—	7	1	no	—
318	D₄	—	7	1	no	—
319	D₄	—	14	2	no	—
320	D₄	—	14	2	no	—
321	D₄	—	14	2	no	—
322	D₄	—	14	1	no	—
323	D₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
324	D₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	7	2	no	—
327	C₂×C₄	—	14	2	no	—
328	C₂×C₄	—	14	2	no	—
329	C₂×C₄	—	14	2	no	—
330	C₂×C₄	—	14	1	no	—
331	C₂×C₄	—	14	1	no	—
332	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
333	C₈	—	7	1	no	—
334	C₈	—	7	1	no	—
335	C₈	C₂²×AGL(1,𝔽₇)	1	2	yes	—
336	C₇	C₃×#577	1	1	yes	characteristic, complemented, Sylow
337	C₂×C₃	—	7	1	no	—
338	C₂×C₃	—	14	1	no	—
339	C₂×C₃	—	14	2	no	—
340	C₂×C₃	—	28	2	no	—
341	C₂×C₃	—	28	1	no	—
342	C₂×C₃	—	28	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	7	2	no	—
346	C₂²	—	8	1	no	—
347	C₂²	—	14	1	no	—
348	C₂²	—	56	2	no	—
349	C₂²	D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	7	2	no	—
352	C₄	—	14	1	no	—
353	C₄	—	14	2	no	—
354	C₄	D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
355	C₄	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
356	C₃	—	7	1	no	Sylow
357	C₂	—	2	1	no	—
358	C₂	—	4	2	no	—
359	C₂	—	4	1	no	—
360	C₂	—	14	2	no	—
361	C₂	—	28	1	no	—
362	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×#577
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. #10621519	C₂	semidirect
2. #6548⋊C₃	C₂	semidirect
3. ΓL(1,𝔽₈)×AGL(1,ℤ/8)	C₂	semidirect
4. #6513⋊C₃	C₂	semidirect
5. C₂×#1142⋊C₃	C₂	semidirect
6. #6478⋊C₃	C₂	semidirect
7. SD₁₆×AGL(1,𝔽₇)	C₂	semidirect
8. #6475⋊C₃	C₂	semidirect
9. #6474⋊C₃	C₂	semidirect
10. #6472⋊C₃	C₂	semidirect
11. #6470⋊C₃	C₂	semidirect
12. #90466	C₃	semidirect
13. #41×ΓL(1,𝔽₈)	C₂²	semidirect
16. Q₈×AGL(1,𝔽₇)	C₂²	semidirect
20. #1159⋊C₃	C₂²	semidirect
27. C₂×ΓL(1,𝔽₈)⋊Q₈	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. #1142⋊C₃	C₂²	semidirect
35. #1142⋊C₃	C₂²	semidirect
36. #1141⋊C₃	C₂²	semidirect
37. C₂×ΓL(1,𝔽₈)⋊C₈	C₂²	semidirect
38. Dic₂₈⋊C₃	C₂²	semidirect
39. #1132⋊C₃	C₂²	semidirect
40. #1131⋊C₃	C₂²	semidirect
41. C₈×AGL(1,𝔽₇)	C₂²	semidirect
42. #6554	C₂×C₃	semidirect
43. #6548	C₂×C₃	semidirect
44. C₇×AGL(1,ℤ/8)	C₂×C₃	semidirect
45. #6513	C₂×C₃	semidirect
46. C₂×#1142	C₂×C₃	semidirect
47. #6478	C₂×C₃	semidirect
48. D₇×SD₁₆	C₂×C₃	semidirect
49. #6475	C₂×C₃	semidirect
50. #6474	C₂×C₃	semidirect
51. #6472	C₂×C₃	semidirect
52. #6470	C₂×C₃	semidirect
84. C₇×#41	C₂²×C₃	semidirect
87. Q₈×D₇	C₂²×C₃	semidirect
91. #1159	C₂²×C₃	semidirect
98. C₂×Dic₁₄	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. #1142	C₂²×C₃	semidirect
106. #1142	C₂²×C₃	semidirect
107. #1141	C₂²×C₃	semidirect
108. C₂×C₇⋊C₈	C₂²×C₃	semidirect
109. Dic₂₈	C₂²×C₃	semidirect
110. #1132	C₂²×C₃	semidirect
111. #1131	C₂²×C₃	semidirect
112. C₈×D₇	C₂²×C₃	semidirect
208. AGL(1,ℤ/8)	AGL(1,𝔽₇)	semidirect
257. ΓL(1,𝔽₈)	#577	semidirect
265. #41	C₂×AGL(1,𝔽₇)	semidirect
280. SD₁₆	C₂×AGL(1,𝔽₇)	semidirect
282. D₈	C₂×AGL(1,𝔽₇)	semidirect
284. M₁₆	C₂×AGL(1,𝔽₇)	semidirect
336. C₇	C₃×#577	semidirect

Maximal subgroups

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

subgroup	index
#10621519	2
#6548⋊C₃	2
ΓL(1,𝔽₈)×AGL(1,ℤ/8)	2
#6513⋊C₃	2
C₂×#1142⋊C₃	2
#6478⋊C₃	2
SD₁₆×AGL(1,𝔽₇)	2
#6475⋊C₃	2
#6474⋊C₃	2
#6472⋊C₃	2
#6470⋊C₃	2
#90466	3
C₃×#577	7

Subgroups — #90466⋊C3 #13057509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #90466⋊C₃ #13057509