Subgroups — #90237⋊C₃ #13057283

Order 1344.

588 conjugacy classes of subgroups.

The subgroup lattice has 308 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	1	yes	maximal, characteristic
2	C₄×D₄×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×ΓL(1,𝔽₈)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×(C₂²⋊D₇)⋊C₃	C₂	1	2	yes	maximal, complemented
5	C₂×(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₄⋊C₄×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
7	#6450⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	1	2	yes	maximal, complemented
9	#6440⋊C₃	C₂	1	2	yes	maximal, complemented
10	#6435⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×ΓL(1,𝔽₈)⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#90237	C₃	1	1	yes	maximal, characteristic, complemented, Hall
13	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
14	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
15	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	—
16	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
17	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
18	#1159⋊C₃	C₄	1	8	yes	complemented
19	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	—
20	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
21	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
23	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
24	C₄²×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
25	(C₂²⋊Dic₇)⋊C₃	C₂²	1	2	yes	—
26	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic
27	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic
28	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	1	yes	characteristic
29	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	—
30	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
31	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
32	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	—
33	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	—
34	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
35	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
37	C₂×#1159	C₂×C₃	1	1	yes	characteristic
38	C₄×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
39	D₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
40	C₄×C₂²⋊D₇	C₂×C₃	1	2	yes	complemented
41	C₂×Dic₇⋊C₄	C₂×C₃	1	2	yes	complemented
42	D₇×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
43	#6450	C₂×C₃	1	1	yes	characteristic, complemented
44	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
45	#6440	C₂×C₃	1	2	yes	complemented
46	#6435	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×Dic₁₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₃×#520	—	7	1	no	maximal, Hall
49	C₂³×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
50	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
51	D₄×ΓL(1,𝔽₈)	C₂×C₄	1	4	yes	complemented
52	C₂×C₄×ΓL(1,𝔽₈)	—	4	2	no	—
53	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
54	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
55	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
56	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
57	(C₂²⋊D₇)⋊C₃	C₂×C₄	1	8	yes	complemented
58	C₂×ΓL(1,𝔽₈)⋊C₄	—	4	2	no	—
59	C₂×ΓL(1,𝔽₈)⋊C₄	C₂×C₄	1	8	yes	complemented
60	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
61	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
64	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
65	C₄×AGL(1,𝔽₇)	—	4	2	no	—
66	C₄×AGL(1,𝔽₇)	C₂×C₄	1	4	yes	complemented
67	ΓL(1,𝔽₈)⋊Q₈	C₂×C₄	1	4	yes	complemented
68	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	—
70	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
71	C₂²×Dic₇	C₂²×C₃	1	2	yes	—
72	C₂²×Dic₇	C₂²×C₃	1	2	yes	—
73	#1159	C₃×C₄	1	8	yes	complemented
74	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
75	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
76	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
77	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic
80	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	—
81	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
82	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
84	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
85	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
88	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
89	C₄×Dic₇	C₂²×C₃	1	2	yes	—
90	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
91	C₄×Dic₇	C₂²×C₃	1	2	yes	—
92	C₂×C₃×#41	—	7	1	no	—
93	C₃×C₄×Q₈	—	7	1	no	—
94	C₃×C₄×Q₈	—	7	1	no	—
95	C₃×C₄×D₄	—	7	2	no	—
96	C₃×C₄×D₄	—	7	2	no	—
97	C₃×C₄×D₄	—	7	1	no	—
98	C₃×C₄×D₄	—	7	1	no	—
99	C₃×#117	—	7	1	no	—
100	C₃×#117	—	7	2	no	—
101	C₂×C₃×C₄⋊C₄	—	7	1	no	—
102	C₂×C₃×C₄⋊C₄	—	7	2	no	—
103	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
104	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
105	C₂²×ΓL(1,𝔽₈)	C₂²×C₄	1	4	yes	—
106	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
107	C₂×AGL(1,𝔽₇)	—	2	1	no	—
108	C₂×AGL(1,𝔽₇)	—	2	1	no	—
109	C₂×AGL(1,𝔽₇)	C₂²×C₄	1	2	yes	—
110	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
111	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
112	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
113	C₄×ΓL(1,𝔽₈)	C₂²×C₄	1	2	yes	—
114	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
115	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
116	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
117	ΓL(1,𝔽₈)⋊C₄	C₂²×C₄	1	4	yes	—
118	ΓL(1,𝔽₈)⋊C₄	C₂²×C₄	1	2	yes	—
119	#520	—	7	1	no	Sylow
120	C₂³×C₇	C₂³×C₃	1	2	yes	—
121	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
122	C₇×D₄	C₂×C₃×C₄	1	4	yes	complemented
123	C₂×C₄×C₇	—	4	2	no	—
124	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
125	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
126	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
127	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
128	C₂²⋊D₇	C₂×C₃×C₄	1	8	yes	complemented
129	C₂×Dic₇	—	4	2	no	—
130	C₂×Dic₇	C₂×C₃×C₄	1	8	yes	complemented
131	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
132	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
133	C₂×Dic₇	C₂³×C₃	1	2	yes	—
134	C₂×Dic₇	C₂³×C₃	1	2	yes	—
135	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
136	C₄×D₇	—	4	2	no	—
137	C₄×D₇	C₂×C₃×C₄	1	4	yes	complemented
138	Dic₁₄	C₂×C₃×C₄	1	4	yes	complemented
139	C₃×#41	—	7	8	no	—
140	C₂×C₃×Q₈	—	7	1	no	—
141	C₂×C₃×D₄	—	7	2	no	—
142	C₂×C₃×D₄	—	7	1	no	—
143	C₂²×C₃×C₄	—	7	1	no	—
144	C₂²×C₃×C₄	—	7	2	no	—
145	C₂²×C₃×C₄	—	7	2	no	—
146	C₂²×C₃×C₄	—	7	2	no	—
147	C₂²×C₃×C₄	—	7	2	no	—
148	C₃×C₄⋊C₄	—	7	2	no	—
149	C₃×C₄⋊C₄	—	7	1	no	—
150	C₃×C₄⋊C₄	—	7	2	no	—
151	C₃×C₄⋊C₄	—	7	2	no	—
152	C₃×C₄⋊C₄	—	7	1	no	—
153	C₃×C₄⋊C₄	—	7	1	no	—
154	C₃×C₄⋊C₄	—	7	1	no	—
155	C₃×C₂²⋊C₄	—	7	1	no	—
156	C₃×C₂²⋊C₄	—	7	1	no	—
157	C₃×C₂²⋊C₄	—	7	2	no	—
158	C₃×C₂²⋊C₄	—	7	2	no	—
159	C₃×C₄²	—	7	2	no	—
160	C₃×C₄²	—	7	2	no	—
161	C₃×C₄²	—	7	1	no	—
162	C₃×C₄²	—	7	1	no	—
163	C₂×ΓL(1,𝔽₈)	—	2	4	no	—
164	C₂×ΓL(1,𝔽₈)	C₂³×C₄	1	1	yes	characteristic
165	C₂×ΓL(1,𝔽₈)	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×ΓL(1,𝔽₈)	2₋¹⁺⁴	1	1	yes	characteristic
167	AGL(1,𝔽₇)	—	2	2	no	—
168	C₂×#41	—	7	1	no	—
169	C₄×Q₈	—	7	1	no	—
170	C₄×Q₈	—	7	1	no	—
171	C₄×D₄	—	7	1	no	—
172	C₄×D₄	—	7	2	no	—
173	C₄×D₄	—	7	2	no	—
174	C₄×D₄	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
175	#117	—	7	2	no	—
176	#117	—	7	1	no	—
177	C₂×C₄⋊C₄	—	7	2	no	—
178	C₂×C₄⋊C₄	—	7	1	no	—
179	C₂²×C₇	—	2	2	no	—
180	C₂²×C₇	—	2	2	no	—
181	C₂²×C₇	C₂²×C₃×C₄	1	4	yes	—
182	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
183	C₂×D₇	—	2	1	no	—
184	C₂×D₇	—	2	1	no	—
185	C₂×D₇	C₂²×C₃×C₄	1	2	yes	—
186	C₄×C₇	—	2	2	no	—
187	C₄×C₇	—	2	1	no	—
188	C₄×C₇	—	2	1	no	—
189	C₄×C₇	C₂²×C₃×C₄	1	2	yes	—
190	Dic₇	—	2	2	no	—
191	Dic₇	—	2	1	no	—
192	Dic₇	—	2	1	no	—
193	Dic₇	C₂²×C₃×C₄	1	4	yes	—
194	Dic₇	C₂²×C₃×C₄	1	2	yes	—
195	C₂³×C₃	—	7	1	no	—
196	C₂³×C₃	—	7	2	no	—
197	C₃×Q₈	—	7	4	no	—
198	C₃×D₄	—	7	8	no	—
199	C₃×D₄	—	7	4	no	—
200	C₂×C₃×C₄	—	7	4	no	—
201	C₂×C₃×C₄	—	7	8	no	—
202	C₂×C₃×C₄	—	7	2	no	—
203	C₂×C₃×C₄	—	7	1	no	—
204	C₂×C₃×C₄	—	7	1	no	—
205	C₂×C₃×C₄	—	7	2	no	—
206	C₂×C₃×C₄	—	7	1	no	—
207	C₂×C₃×C₄	—	7	1	no	—
208	C₂×C₃×C₄	—	7	1	no	—
209	C₂×C₃×C₄	—	7	2	no	—
210	C₂×C₃×C₄	—	7	1	no	—
211	C₂×C₃×C₄	—	28	2	no	—
212	C₂×C₃×C₄	—	28	2	no	—
213	C₂×C₃×C₄	—	28	2	no	—
214	ΓL(1,𝔽₈)	#520	1	1	yes	characteristic, complemented, Hall
215	#41	—	7	8	no	—
216	C₂×Q₈	—	7	1	no	—
217	C₂×D₄	—	7	2	no	—
218	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
219	C₂²×C₄	—	7	2	no	—
220	C₂²×C₄	—	7	1	no	—
221	C₂²×C₄	—	7	2	no	—
222	C₂²×C₄	—	7	2	no	—
223	C₂²×C₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
224	C₄⋊C₄	—	7	2	no	—
225	C₄⋊C₄	—	7	1	no	—
226	C₄⋊C₄	—	7	2	no	—
227	C₄⋊C₄	—	7	2	no	—
228	C₄⋊C₄	—	7	1	no	—
229	C₄⋊C₄	—	7	1	no	—
230	C₄⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
231	C₂²⋊C₄	—	7	2	no	—
232	C₂²⋊C₄	—	7	1	no	—
233	C₂²⋊C₄	—	7	1	no	—
234	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
235	C₄²	—	7	2	no	—
236	C₄²	—	7	2	no	—
237	C₄²	—	7	1	no	—
238	C₄²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
239	C₂×C₇	—	2	4	no	—
240	C₂×C₇	C₂³×C₃×C₄	1	1	yes	characteristic
241	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₇	C₃×2₋¹⁺⁴	1	1	yes	characteristic
243	D₇	—	2	2	no	—
244	C₂²×C₃	—	7	2	no	—
245	C₂²×C₃	—	7	4	no	—
246	C₂²×C₃	—	7	1	no	—
247	C₂²×C₃	—	14	2	no	—
248	C₂²×C₃	—	14	2	no	—
249	C₂²×C₃	—	14	1	no	—
250	C₂²×C₃	—	14	1	no	—
251	C₃×C₄	—	7	2	no	—
252	C₃×C₄	—	7	4	no	—
253	C₃×C₄	—	7	2	no	—
254	C₃×C₄	—	14	1	no	—
255	C₃×C₄	—	14	2	no	—
256	C₃×C₄	—	14	1	no	—
257	C₃×C₄	—	14	2	no	—
258	C₃×C₄	—	14	1	no	—
259	C₃×C₄	—	14	1	no	—
260	C₂³	—	7	1	no	—
261	C₂³	C₂²×AGL(1,𝔽₇)	1	2	yes	—
262	Q₈	—	7	4	no	—
263	D₄	—	7	8	no	—
264	D₄	C₄×AGL(1,𝔽₇)	1	4	yes	complemented
265	C₂×C₄	—	4	2	no	—
266	C₂×C₄	—	7	8	no	—
267	C₂×C₄	—	7	2	no	—
268	C₂×C₄	—	7	1	no	—
269	C₂×C₄	—	7	4	no	—
270	C₂×C₄	—	7	1	no	—
271	C₂×C₄	—	7	2	no	—
272	C₂×C₄	—	7	1	no	—
273	C₂×C₄	—	28	2	no	—
274	C₂×C₄	—	28	2	no	—
275	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
276	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
277	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
278	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
279	C₇	C₃×#520	1	1	yes	characteristic, complemented, Sylow
280	C₂×C₃	—	7	1	no	—
281	C₂×C₃	—	7	1	no	—
282	C₂×C₃	—	7	1	no	—
283	C₂×C₃	—	14	4	no	—
284	C₂×C₃	—	14	2	no	—
285	C₂²	—	2	2	no	—
286	C₂²	—	2	2	no	—
287	C₂²	—	7	2	no	—
288	C₂²	—	14	1	no	—
289	C₂²	—	14	1	no	—
290	C₂²	C₂×C₄×AGL(1,𝔽₇)	1	4	yes	—
291	C₂²	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
292	C₄	—	2	1	no	—
293	C₄	—	2	2	no	—
294	C₄	—	2	1	no	—
295	C₄	—	7	2	no	—
296	C₄	—	7	4	no	—
297	C₄	—	14	2	no	—
298	C₄	—	14	1	no	—
299	C₄	—	14	1	no	—
300	C₄	C₂×C₄×AGL(1,𝔽₇)	1	2	yes	—
301	C₃	—	7	1	no	Sylow
302	C₂	—	2	4	no	—
303	C₂	—	14	2	no	—
304	C₂	C₂²×C₄×AGL(1,𝔽₇)	1	1	yes	characteristic
305	C₂	#6548⋊C₃	1	1	yes	characteristic
306	C₂	#10621519	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×AGL(1,𝔽₇)
commutator	C₂×C₇	C₂³×C₃×C₄
Fitting	C₄×C₇×D₄	C₂×C₃
socle, cosocle	C₂²×C₇	C₂⁴×C₃
prime radical	C₂×#1159⋊C₃	C₂
hypercenter	C₄×D₄	AGL(1,𝔽₇)
hypocenter	C₇	C₃×#520
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₄×D₄×ΓL(1,𝔽₈)	C₂	semidirect
3. D₄×ΓL(1,𝔽₈)⋊C₄	C₂	semidirect
4. C₄×(C₂²⋊D₇)⋊C₃	C₂	semidirect
5. C₂×(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂	semidirect
6. C₄⋊C₄×AGL(1,𝔽₇)	C₂	semidirect
7. #6450⋊C₃	C₂	semidirect
8. ((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	semidirect
9. #6440⋊C₃	C₂	semidirect
10. #6435⋊C₃	C₂	semidirect
11. C₄×ΓL(1,𝔽₈)⋊Q₈	C₂	semidirect
12. #90237	C₃	semidirect
18. #1159⋊C₃	C₄	semidirect
38. C₄×C₇×D₄	C₂×C₃	semidirect
39. D₄×Dic₇	C₂×C₃	semidirect
40. C₄×C₂²⋊D₇	C₂×C₃	semidirect
41. C₂×Dic₇⋊C₄	C₂×C₃	semidirect
42. D₇×C₄⋊C₄	C₂×C₃	semidirect
43. #6450	C₂×C₃	semidirect
44. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
45. #6440	C₂×C₃	semidirect
46. #6435	C₂×C₃	semidirect
47. C₄×Dic₁₄	C₂×C₃	semidirect
51. D₄×ΓL(1,𝔽₈)	C₂×C₄	semidirect
57. (C₂²⋊D₇)⋊C₃	C₂×C₄	semidirect
59. C₂×ΓL(1,𝔽₈)⋊C₄	C₂×C₄	semidirect
66. C₄×AGL(1,𝔽₇)	C₂×C₄	semidirect
67. ΓL(1,𝔽₈)⋊Q₈	C₂×C₄	semidirect
73. #1159	C₃×C₄	semidirect
122. C₇×D₄	C₂×C₃×C₄	semidirect
128. C₂²⋊D₇	C₂×C₃×C₄	semidirect
130. C₂×Dic₇	C₂×C₃×C₄	semidirect
137. C₄×D₇	C₂×C₃×C₄	semidirect
138. Dic₁₄	C₂×C₃×C₄	semidirect
174. C₄×D₄	AGL(1,𝔽₇)	semidirect
214. ΓL(1,𝔽₈)	#520	semidirect
264. D₄	C₄×AGL(1,𝔽₇)	semidirect
279. C₇	C₃×#520	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
C₄×D₄×ΓL(1,𝔽₈)	2
D₄×ΓL(1,𝔽₈)⋊C₄	2
C₄×(C₂²⋊D₇)⋊C₃	2
C₂×(ΓL(1,𝔽₈)⋊C₄)⋊C₄	2
C₄⋊C₄×AGL(1,𝔽₇)	2
#6450⋊C₃	2
((C₂²⋊D₇)⋊C₃)⋊C₄	2
#6440⋊C₃	2
#6435⋊C₃	2
C₄×ΓL(1,𝔽₈)⋊Q₈	2
#90237	3
C₃×#520	7

Subgroups — #90237⋊C3 #13057283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #90237⋊C₃ #13057283