Subgroups — #90287⋊C₃ #13057330

Order 1344.

620 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1159⋊C₃	C₂	1	2	yes	maximal, complemented
2	ΓL(1,𝔽₈)×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	#6503⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#6502⋊C₃	C₂	1	2	yes	maximal, complemented
5	D₄×ΓL(1,𝔽₈)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#6493⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×ΓL(1,𝔽₈)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	#6456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#6451⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#6448⋊C₃	C₂	1	2	yes	maximal, complemented
11	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	1	2	yes	maximal, complemented
12	#90287	C₃	1	1	yes	maximal, characteristic, complemented, Hall
13	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
14	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
15	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
16	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	—
17	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	—
18	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	—
19	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
20	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
22	#1159⋊C₃	—	2	8	no	—
23	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
24	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	—
25	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	2	yes	—
26	C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
27	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
28	(C₂²⋊Dic₇)⋊C₃	C₂²	1	2	yes	—
29	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	—
30	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	—
31	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	1	yes	characteristic
32	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	—
33	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×#1159	C₂×C₃	1	2	yes	complemented
38	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
39	#6503	C₂×C₃	1	1	yes	characteristic, complemented
40	#6502	C₂×C₃	1	2	yes	complemented
41	D₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
42	#6493	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
44	#6456	C₂×C₃	1	1	yes	characteristic, complemented
45	#6451	C₂×C₃	1	1	yes	characteristic, complemented
46	#6448	C₂×C₃	1	2	yes	complemented
47	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
48	C₃×#532	—	7	1	no	maximal, Hall
49	C₂³×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
50	C₂³×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
51	C₂²×AGL(1,𝔽₇)	C₂³	1	2	yes	—
52	D₄×ΓL(1,𝔽₈)	—	2	4	no	—
53	D₄×ΓL(1,𝔽₈)	—	2	2	no	—
54	C₂×C₄×ΓL(1,𝔽₈)	—	2	2	no	—
55	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
56	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
57	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
58	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
59	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
60	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
61	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	4	no	—
62	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
63	C₂×ΓL(1,𝔽₈)⋊C₄	D₄	1	4	yes	complemented
64	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
65	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
69	C₄⋊AGL(1,𝔽₇)	—	2	2	no	—
70	C₄×AGL(1,𝔽₇)	—	2	4	no	—
71	ΓL(1,𝔽₈)⋊Q₈	—	2	4	no	—
72	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₇×D₄	C₂²×C₃	1	2	yes	—
74	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
76	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
77	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
78	C₂²×Dic₇	C₂²×C₃	1	2	yes	—
79	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
80	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
81	#1159	—	2	8	no	—
82	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
84	C₂×Dic₁₄	C₂²×C₃	1	2	yes	—
85	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	—
88	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
89	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
90	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
91	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
92	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
93	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
94	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
95	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×#41	—	7	2	no	—
97	C₃×C₄⋊Q₈	—	7	1	no	—
98	C₃×#127	—	7	1	no	—
99	C₃×#124	—	7	2	no	—
100	C₃×#121	—	7	1	no	—
101	C₃×#121	—	7	2	no	—
102	C₃×#121	—	7	1	no	—
103	C₃×C₄×D₄	—	7	2	no	—
104	C₃×C₄×D₄	—	7	1	no	—
105	C₃×C₄×D₄	—	7	1	no	—
106	C₂×C₃×C₄²	—	7	1	no	—
107	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
108	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
109	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
110	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
111	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
112	C₂²×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	—
113	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
114	C₂×AGL(1,𝔽₇)	—	2	2	no	—
115	C₂×AGL(1,𝔽₇)	—	2	2	no	—
116	C₂×AGL(1,𝔽₇)	—	2	2	no	—
117	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
118	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
119	C₄×ΓL(1,𝔽₈)	#41	1	2	yes	complemented
120	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
121	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
122	ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	2	yes	—
123	ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	2	yes	—
124	ΓL(1,𝔽₈)⋊C₄	#41	1	2	yes	complemented
125	#532	—	7	1	no	Sylow
126	C₂³×C₇	C₂³×C₃	1	2	yes	—
127	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
128	C₂²×D₇	C₂³×C₃	1	2	yes	—
129	C₇×D₄	—	2	4	no	—
130	C₇×D₄	—	2	2	no	—
131	C₂×C₄×C₇	—	2	2	no	—
132	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
134	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
135	C₂²⋊D₇	—	2	4	no	—
136	C₂²⋊D₇	—	2	4	no	—
137	C₂²⋊D₇	—	2	4	no	—
138	C₂×Dic₇	—	2	4	no	—
139	C₂×Dic₇	—	2	2	no	—
140	C₂×Dic₇	C₃×D₄	1	4	yes	complemented
141	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
142	C₂×Dic₇	C₂³×C₃	1	2	yes	—
143	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
144	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
145	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
146	D₂₈	—	2	2	no	—
147	C₄×D₇	—	2	4	no	—
148	Dic₁₄	—	2	4	no	—
149	C₃×#41	—	14	8	no	—
150	C₂×C₃×Q₈	—	7	2	no	—
151	C₂×C₃×D₄	—	7	1	no	—
152	C₂×C₃×D₄	—	7	2	no	—
153	C₂×C₃×D₄	—	7	2	no	—
154	C₂×C₃×D₄	—	7	2	no	—
155	C₂×C₃×D₄	—	7	1	no	—
156	C₂×C₃×D₄	—	7	2	no	—
157	C₂²×C₃×C₄	—	7	1	no	—
158	C₂²×C₃×C₄	—	7	2	no	—
159	C₂²×C₃×C₄	—	7	1	no	—
160	C₂²×C₃×C₄	—	7	2	no	—
161	C₂²×C₃×C₄	—	7	1	no	—
162	C₃×C₄⋊C₄	—	7	2	no	—
163	C₃×C₄⋊C₄	—	7	1	no	—
164	C₃×C₄⋊C₄	—	7	1	no	—
165	C₃×C₂²⋊C₄	—	7	2	no	—
166	C₃×C₂²⋊C₄	—	7	2	no	—
167	C₃×C₂²⋊C₄	—	7	2	no	—
168	C₃×C₂²⋊C₄	—	7	2	no	—
169	C₃×C₄²	—	7	1	no	—
170	C₃×C₄²	—	7	1	no	—
171	C₃×C₄²	—	7	1	no	—
172	C₃×C₄²	—	7	1	no	—
173	C₂×ΓL(1,𝔽₈)	—	2	2	no	—
174	C₂×ΓL(1,𝔽₈)	—	4	2	no	—
175	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
176	C₂×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
177	C₂×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
178	AGL(1,𝔽₇)	—	4	2	no	—
179	C₂×#41	—	7	2	no	—
180	C₄⋊Q₈	—	7	1	no	—
181	#127	—	7	1	no	—
182	#124	—	7	2	no	—
183	#121	—	7	2	no	—
184	#121	—	7	1	no	—
185	#121	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
186	C₄×D₄	—	7	1	no	—
187	C₄×D₄	—	7	1	no	—
188	C₄×D₄	—	7	2	no	—
189	C₂×C₄²	—	7	1	no	—
190	C₂²×C₇	—	2	1	no	—
191	C₂²×C₇	—	2	1	no	—
192	C₂²×C₇	—	2	2	no	—
193	C₂²×C₇	—	2	2	no	—
194	C₂²×C₇	—	2	2	no	—
195	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
196	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
197	C₂×D₇	—	2	2	no	—
198	C₂×D₇	—	2	2	no	—
199	C₂×D₇	—	2	2	no	—
200	C₄×C₇	—	2	2	no	—
201	C₄×C₇	—	2	1	no	—
202	C₄×C₇	C₃×#41	1	2	yes	complemented
203	Dic₇	—	2	2	no	—
204	Dic₇	—	2	1	no	—
205	Dic₇	C₂×C₃×D₄	1	2	yes	—
206	Dic₇	C₂×C₃×D₄	1	2	yes	—
207	Dic₇	C₃×#41	1	2	yes	complemented
208	C₂³×C₃	—	7	2	no	—
209	C₂³×C₃	—	7	1	no	—
210	C₂³×C₃	—	7	2	no	—
211	C₃×Q₈	—	14	4	no	—
212	C₃×D₄	—	14	2	no	—
213	C₃×D₄	—	14	4	no	—
214	C₃×D₄	—	14	2	no	—
215	C₃×D₄	—	14	4	no	—
216	C₃×D₄	—	14	4	no	—
217	C₃×D₄	—	14	4	no	—
218	C₂×C₃×C₄	—	7	4	no	—
219	C₂×C₃×C₄	—	7	1	no	—
220	C₂×C₃×C₄	—	7	1	no	—
221	C₂×C₃×C₄	—	7	1	no	—
222	C₂×C₃×C₄	—	7	1	no	—
223	C₂×C₃×C₄	—	7	2	no	—
224	C₂×C₃×C₄	—	7	1	no	—
225	C₂×C₃×C₄	—	7	1	no	—
226	C₂×C₃×C₄	—	7	2	no	—
227	C₂×C₃×C₄	—	14	2	no	—
228	C₂×C₃×C₄	—	14	4	no	—
229	C₂×C₃×C₄	—	14	2	no	—
230	C₂×C₃×C₄	—	14	4	no	—
231	ΓL(1,𝔽₈)	#532	1	1	yes	characteristic, complemented, Hall
232	#41	—	14	8	no	—
233	C₂×Q₈	—	7	2	no	—
234	C₂×D₄	—	7	2	no	—
235	C₂×D₄	—	7	2	no	—
236	C₂×D₄	—	7	2	no	—
237	C₂×D₄	—	7	1	no	—
238	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
239	C₂×D₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
240	C₂²×C₄	—	7	1	no	—
241	C₂²×C₄	—	7	1	no	—
242	C₂²×C₄	—	7	2	no	—
243	C₂²×C₄	—	7	2	no	—
244	C₂²×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
245	C₄⋊C₄	—	7	2	no	—
246	C₄⋊C₄	—	7	1	no	—
247	C₄⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
248	C₂²⋊C₄	—	7	2	no	—
249	C₂²⋊C₄	—	7	2	no	—
250	C₂²⋊C₄	—	7	2	no	—
251	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
252	C₄²	—	7	1	no	—
253	C₄²	—	7	1	no	—
254	C₄²	—	7	1	no	—
255	C₄²	—	7	1	no	—
256	C₂×C₇	—	2	2	no	—
257	C₂×C₇	—	4	2	no	—
258	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
259	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
260	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
261	D₇	—	4	2	no	—
262	C₂²×C₃	—	7	2	no	—
263	C₂²×C₃	—	7	1	no	—
264	C₂²×C₃	—	14	1	no	—
265	C₂²×C₃	—	14	1	no	—
266	C₂²×C₃	—	14	2	no	—
267	C₂²×C₃	—	14	2	no	—
268	C₂²×C₃	—	14	2	no	—
269	C₂²×C₃	—	14	2	no	—
270	C₂²×C₃	—	14	2	no	—
271	C₂²×C₃	—	14	2	no	—
272	C₃×C₄	—	7	2	no	—
273	C₃×C₄	—	7	2	no	—
274	C₃×C₄	—	7	2	no	—
275	C₃×C₄	—	7	2	no	—
276	C₃×C₄	—	14	2	no	—
277	C₃×C₄	—	14	1	no	—
278	C₃×C₄	—	14	2	no	—
279	C₃×C₄	—	14	1	no	—
280	C₂³	—	7	2	no	—
281	C₂³	C₂²×AGL(1,𝔽₇)	1	2	yes	—
282	C₂³	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
283	Q₈	—	14	4	no	—
284	D₄	—	2	4	no	—
285	D₄	—	2	2	no	—
286	D₄	—	14	4	no	—
287	D₄	—	14	4	no	—
288	D₄	—	14	4	no	—
289	D₄	—	14	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	7	4	no	—
292	C₂×C₄	—	7	1	no	—
293	C₂×C₄	—	7	1	no	—
294	C₂×C₄	—	7	1	no	—
295	C₂×C₄	—	7	1	no	—
296	C₂×C₄	—	7	2	no	—
297	C₂×C₄	—	14	4	no	—
298	C₂×C₄	—	14	4	no	—
299	C₂×C₄	—	14	2	no	—
300	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
301	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
302	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
303	C₇	C₃×#532	1	1	yes	characteristic, complemented, Sylow
304	C₂×C₃	—	7	1	no	—
305	C₂×C₃	—	7	1	no	—
306	C₂×C₃	—	7	1	no	—
307	C₂×C₃	—	14	2	no	—
308	C₂×C₃	—	28	2	no	—
309	C₂×C₃	—	28	2	no	—
310	C₂²	—	2	1	no	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	14	2	no	—
316	C₂²	—	14	2	no	—
317	C₂²	—	14	2	no	—
318	C₂²	D₄×AGL(1,𝔽₇)	1	2	yes	—
319	C₂²	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
320	C₄	—	2	2	no	—
321	C₄	—	2	1	no	—
322	C₄	—	7	2	no	—
323	C₄	—	7	2	no	—
324	C₄	—	7	2	no	—
325	C₄	—	14	2	no	—
326	C₄	—	14	1	no	—
327	C₄	#1159⋊C₃	1	2	yes	complemented
328	C₃	—	7	1	no	Sylow
329	C₂	—	2	2	no	—
330	C₂	—	4	2	no	—
331	C₂	—	28	2	no	—
332	C₂	C₂×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
333	C₂	C₂×#1159⋊C₃	1	1	yes	characteristic
334	C₂	#41×AGL(1,𝔽₇)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₇	C₂⁴×C₃
Fitting	C₇×#121	C₂×C₃
hypercenter	#121	AGL(1,𝔽₇)
hypocenter	C₇	C₃×#532
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #121

Complements

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

N	H ≅ G/N	type
1. C₂×#1159⋊C₃	C₂	semidirect
2. ΓL(1,𝔽₈)×#121	C₂	semidirect
3. #6503⋊C₃	C₂	semidirect
4. #6502⋊C₃	C₂	semidirect
5. D₄×ΓL(1,𝔽₈)⋊C₄	C₂	semidirect
6. #6493⋊C₃	C₂	semidirect
7. C₂×C₄×ΓL(1,𝔽₈)⋊C₄	C₂	semidirect
8. #6456⋊C₃	C₂	semidirect
9. #6451⋊C₃	C₂	semidirect
10. #6448⋊C₃	C₂	semidirect
11. ((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	semidirect
12. #90287	C₃	semidirect
37. C₂×#1159	C₂×C₃	semidirect
38. C₇×#121	C₂×C₃	semidirect
39. #6503	C₂×C₃	semidirect
40. #6502	C₂×C₃	semidirect
41. D₄×Dic₇	C₂×C₃	semidirect
42. #6493	C₂×C₃	semidirect
43. C₂×C₄×Dic₇	C₂×C₃	semidirect
44. #6456	C₂×C₃	semidirect
45. #6451	C₂×C₃	semidirect
46. #6448	C₂×C₃	semidirect
47. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
63. C₂×ΓL(1,𝔽₈)⋊C₄	D₄	semidirect
119. C₄×ΓL(1,𝔽₈)	#41	semidirect
124. ΓL(1,𝔽₈)⋊C₄	#41	semidirect
140. C₂×Dic₇	C₃×D₄	semidirect
185. #121	AGL(1,𝔽₇)	semidirect
202. C₄×C₇	C₃×#41	semidirect
207. Dic₇	C₃×#41	semidirect
231. ΓL(1,𝔽₈)	#532	semidirect
303. C₇	C₃×#532	semidirect
327. C₄	#1159⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#1159⋊C₃	2
ΓL(1,𝔽₈)×#121	2
#6503⋊C₃	2
#6502⋊C₃	2
D₄×ΓL(1,𝔽₈)⋊C₄	2
#6493⋊C₃	2
C₂×C₄×ΓL(1,𝔽₈)⋊C₄	2
#6456⋊C₃	2
#6451⋊C₃	2
#6448⋊C₃	2
((C₂²⋊D₇)⋊C₃)⋊C₄	2
#90287	3
C₃×#532	7

Subgroups — #90287⋊C3 #13057330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #90287⋊C₃ #13057330