Subgroups — #90297⋊C₃ #13057342

Order 1344.

660 conjugacy classes of subgroups.

The subgroup lattice has 368 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, complemented
2	C₂²×C₄×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	#6501⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#6500⋊C₃	C₂	1	2	yes	maximal, complemented
6	D₄×ΓL(1,𝔽₈)⋊C₄	C₂	1	2	yes	maximal, complemented
7	#6487⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#6460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#6455⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#6446⋊C₃	C₂	1	2	yes	maximal, complemented
11	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	1	2	yes	maximal, complemented
12	#90297	C₃	1	1	yes	maximal, characteristic, complemented, Hall
13	C₂³×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
14	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
15	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
20	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	complemented
21	#1159⋊C₃	—	2	4	no	—
22	C₂×C₄×AGL(1,𝔽₇)	—	2	4	no	—
23	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
24	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
25	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
26	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
27	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
29	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
30	(C₂²⋊Dic₇)⋊C₃	C₂²	1	2	yes	—
31	(C₂²⋊Dic₇)⋊C₃	C₂²	1	2	yes	complemented
32	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	—
33	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	—
34	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	2	yes	complemented
35	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	1	yes	characteristic, complemented
36	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	complemented
37	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	complemented
38	C₂×#1159	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×C₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
41	#6501	C₂×C₃	1	1	yes	characteristic, complemented
42	#6500	C₂×C₃	1	2	yes	complemented
43	D₄×Dic₇	C₂×C₃	1	2	yes	complemented
44	#6487	C₂×C₃	1	1	yes	characteristic, complemented
45	#6460	C₂×C₃	1	1	yes	characteristic, complemented
46	#6455	C₂×C₃	1	1	yes	characteristic, complemented
47	#6446	C₂×C₃	1	2	yes	complemented
48	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
49	C₃×#525	—	7	1	no	maximal, Hall
50	C₂³×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
51	C₂³×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
52	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
53	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
54	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
55	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
56	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
57	D₄×ΓL(1,𝔽₈)	—	2	4	no	—
58	D₄×ΓL(1,𝔽₈)	—	2	2	no	—
59	C₂×C₄×ΓL(1,𝔽₈)	—	2	2	no	—
60	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
61	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
62	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
63	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
64	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
65	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
66	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	4	no	—
67	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
68	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
70	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
71	C₄×AGL(1,𝔽₇)	—	2	2	no	—
72	C₄×AGL(1,𝔽₇)	—	2	2	no	—
73	C₄×AGL(1,𝔽₇)	—	2	2	no	—
74	C₄×AGL(1,𝔽₇)	D₄	1	4	yes	complemented
75	ΓL(1,𝔽₈)⋊Q₈	—	2	2	no	—
76	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₇×D₄	C₂²×C₃	1	2	yes	—
78	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
81	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
82	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
83	C₂²×Dic₇	C₂²×C₃	1	2	yes	complemented
84	#1159	—	2	4	no	—
85	C₂×C₄×D₇	—	2	4	no	—
86	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
90	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
91	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
92	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
93	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	—
94	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
95	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
96	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
97	C₄⋊Dic₇	C₂²×C₃	1	2	yes	complemented
98	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
99	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
100	C₄×Dic₇	C₂²×C₃	1	2	yes	complemented
101	C₂×C₃×#41	—	7	1	no	—
102	C₂³×C₃×C₄	—	7	1	no	—
103	C₃×#123	—	7	2	no	—
104	C₃×C₂²⋊Q₈	—	7	1	no	—
105	C₃×C₂²⋊Q₈	—	7	1	no	—
106	C₃×#121	—	7	1	no	—
107	C₃×#121	—	7	1	no	—
108	C₃×#120	—	7	2	no	—
109	C₃×C₄×D₄	—	7	2	no	—
110	C₃×C₄×D₄	—	7	2	no	—
111	C₃×#117	—	7	1	no	—
112	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
113	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
114	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
115	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
116	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
117	C₂²×ΓL(1,𝔽₈)	#41	1	2	yes	complemented
118	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
119	C₂×AGL(1,𝔽₇)	—	2	8	no	—
120	C₂×AGL(1,𝔽₇)	—	2	1	no	—
121	C₂×AGL(1,𝔽₇)	—	2	1	no	—
122	C₂×AGL(1,𝔽₇)	—	2	1	no	—
123	C₂×AGL(1,𝔽₇)	—	2	1	no	—
124	C₂×AGL(1,𝔽₇)	C₂×D₄	1	2	yes	—
125	C₂×AGL(1,𝔽₇)	#41	1	2	yes	complemented
126	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
127	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
128	C₄×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	—
129	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
130	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
131	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
132	ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	2	yes	—
133	#525	—	7	1	no	Sylow
134	C₂³×C₇	C₂³×C₃	1	2	yes	—
135	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
136	C₂²×D₇	—	2	2	no	—
137	C₂²×D₇	—	2	2	no	—
138	C₂²×D₇	—	2	2	no	—
139	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
140	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
141	C₇×D₄	—	2	4	no	—
142	C₇×D₄	—	2	2	no	—
143	C₂×C₄×C₇	—	2	2	no	—
144	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
145	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
147	C₂²⋊D₇	—	2	4	no	—
148	C₂²⋊D₇	—	2	4	no	—
149	C₂×Dic₇	—	2	2	no	—
150	C₂×Dic₇	—	2	4	no	—
151	C₂×Dic₇	C₂³×C₃	1	2	yes	—
152	C₂×Dic₇	C₂³×C₃	1	2	yes	—
153	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
154	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
155	C₄×D₇	—	2	2	no	—
156	C₄×D₇	—	2	2	no	—
157	C₄×D₇	—	2	2	no	—
158	C₄×D₇	C₃×D₄	1	4	yes	complemented
159	Dic₁₄	—	2	2	no	—
160	C₂⁴×C₃	—	7	1	no	—
161	C₃×#41	—	14	4	no	—
162	C₂×C₃×Q₈	—	7	1	no	—
163	C₂×C₃×D₄	—	7	2	no	—
164	C₂×C₃×D₄	—	7	2	no	—
165	C₂×C₃×D₄	—	7	2	no	—
166	C₂×C₃×D₄	—	7	1	no	—
167	C₂²×C₃×C₄	—	7	1	no	—
168	C₂²×C₃×C₄	—	7	1	no	—
169	C₂²×C₃×C₄	—	7	1	no	—
170	C₂²×C₃×C₄	—	7	1	no	—
171	C₂²×C₃×C₄	—	7	1	no	—
172	C₂²×C₃×C₄	—	7	2	no	—
173	C₂²×C₃×C₄	—	7	1	no	—
174	C₂²×C₃×C₄	—	14	4	no	—
175	C₃×C₄⋊C₄	—	7	1	no	—
176	C₃×C₄⋊C₄	—	7	2	no	—
177	C₃×C₄⋊C₄	—	7	2	no	—
178	C₃×C₄⋊C₄	—	7	1	no	—
179	C₃×C₂²⋊C₄	—	7	2	no	—
180	C₃×C₂²⋊C₄	—	7	2	no	—
181	C₃×C₂²⋊C₄	—	7	2	no	—
182	C₃×C₂²⋊C₄	—	7	2	no	—
183	C₃×C₂²⋊C₄	—	7	2	no	—
184	C₃×C₄²	—	7	2	no	—
185	C₂×ΓL(1,𝔽₈)	—	2	2	no	—
186	C₂×ΓL(1,𝔽₈)	—	4	2	no	—
187	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
188	C₂×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
189	C₂×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
190	AGL(1,𝔽₇)	—	2	2	no	—
191	AGL(1,𝔽₇)	—	2	2	no	—
192	C₂×#41	—	7	1	no	—
193	C₂³×C₄	—	7	1	no	—
194	#123	—	7	2	no	—
195	C₂²⋊Q₈	—	7	1	no	—
196	C₂²⋊Q₈	—	7	1	no	—
197	#121	—	7	1	no	—
198	#121	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
199	#120	—	7	2	no	—
200	C₄×D₄	—	7	2	no	—
201	C₄×D₄	—	7	2	no	—
202	#117	—	7	1	no	—
203	C₂²×C₇	—	2	1	no	—
204	C₂²×C₇	—	2	1	no	—
205	C₂²×C₇	—	2	2	no	—
206	C₂²×C₇	—	2	2	no	—
207	C₂²×C₇	—	2	2	no	—
208	C₂²×C₇	C₃×#41	1	2	yes	complemented
209	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
210	C₂×D₇	—	2	8	no	—
211	C₂×D₇	—	2	1	no	—
212	C₂×D₇	—	2	1	no	—
213	C₂×D₇	—	2	1	no	—
214	C₂×D₇	—	2	1	no	—
215	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
216	C₂×D₇	C₃×#41	1	2	yes	complemented
217	C₄×C₇	—	2	1	no	—
218	C₄×C₇	—	2	2	no	—
219	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
220	Dic₇	—	2	2	no	—
221	Dic₇	—	2	1	no	—
222	Dic₇	—	2	2	no	—
223	Dic₇	C₂×C₃×D₄	1	2	yes	—
224	C₂³×C₃	—	7	1	no	—
225	C₂³×C₃	—	7	1	no	—
226	C₂³×C₃	—	7	1	no	—
227	C₂³×C₃	—	7	2	no	—
228	C₂³×C₃	—	14	2	no	—
229	C₂³×C₃	—	14	2	no	—
230	C₂³×C₃	—	14	2	no	—
231	C₃×Q₈	—	14	2	no	—
232	C₃×D₄	—	14	2	no	—
233	C₃×D₄	—	14	4	no	—
234	C₃×D₄	—	14	4	no	—
235	C₃×D₄	—	14	4	no	—
236	C₂×C₃×C₄	—	7	4	no	—
237	C₂×C₃×C₄	—	7	1	no	—
238	C₂×C₃×C₄	—	7	2	no	—
239	C₂×C₃×C₄	—	7	1	no	—
240	C₂×C₃×C₄	—	7	2	no	—
241	C₂×C₃×C₄	—	7	1	no	—
242	C₂×C₃×C₄	—	7	2	no	—
243	C₂×C₃×C₄	—	7	1	no	—
244	C₂×C₃×C₄	—	14	2	no	—
245	C₂×C₃×C₄	—	14	2	no	—
246	C₂×C₃×C₄	—	14	2	no	—
247	C₂×C₃×C₄	—	14	2	no	—
248	C₂×C₃×C₄	—	14	4	no	—
249	C₂×C₃×C₄	—	14	2	no	—
250	ΓL(1,𝔽₈)	#525	1	1	yes	characteristic, complemented, Hall
251	C₂⁴	—	7	1	no	—
252	#41	—	14	4	no	—
253	C₂×Q₈	—	7	1	no	—
254	C₂×D₄	—	7	2	no	—
255	C₂×D₄	—	7	2	no	—
256	C₂×D₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
257	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
258	C₂²×C₄	—	7	1	no	—
259	C₂²×C₄	—	7	1	no	—
260	C₂²×C₄	—	7	2	no	—
261	C₂²×C₄	—	7	1	no	—
262	C₂²×C₄	—	7	1	no	—
263	C₂²×C₄	—	7	1	no	—
264	C₂²×C₄	—	14	4	no	—
265	C₂²×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
266	C₄⋊C₄	—	7	2	no	—
267	C₄⋊C₄	—	7	1	no	—
268	C₄⋊C₄	—	7	2	no	—
269	C₄⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
270	C₂²⋊C₄	—	7	2	no	—
271	C₂²⋊C₄	—	7	2	no	—
272	C₂²⋊C₄	—	7	2	no	—
273	C₂²⋊C₄	—	7	2	no	—
274	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
275	C₄²	—	7	2	no	—
276	C₂×C₇	—	2	2	no	—
277	C₂×C₇	—	4	2	no	—
278	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
279	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
280	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
281	D₇	—	2	2	no	—
282	D₇	—	2	2	no	—
283	C₂²×C₃	—	7	2	no	—
284	C₂²×C₃	—	7	2	no	—
285	C₂²×C₃	—	7	2	no	—
286	C₂²×C₃	—	7	1	no	—
287	C₂²×C₃	—	14	1	no	—
288	C₂²×C₃	—	14	1	no	—
289	C₂²×C₃	—	14	2	no	—
290	C₂²×C₃	—	14	2	no	—
291	C₂²×C₃	—	14	2	no	—
292	C₂²×C₃	—	14	1	no	—
293	C₂²×C₃	—	14	1	no	—
294	C₂²×C₃	—	14	1	no	—
295	C₂²×C₃	—	14	1	no	—
296	C₂²×C₃	—	14	8	no	—
297	C₃×C₄	—	7	2	no	—
298	C₃×C₄	—	7	2	no	—
299	C₃×C₄	—	14	1	no	—
300	C₃×C₄	—	14	2	no	—
301	C₃×C₄	—	14	1	no	—
302	C₃×C₄	—	14	2	no	—
303	C₃×C₄	—	14	2	no	—
304	C₂³	—	7	1	no	—
305	C₂³	—	7	1	no	—
306	C₂³	—	14	2	no	—
307	C₂³	—	14	2	no	—
308	C₂³	—	14	2	no	—
309	C₂³	C₂²×AGL(1,𝔽₇)	1	2	yes	—
310	C₂³	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
311	Q₈	—	14	2	no	—
312	D₄	—	2	4	no	—
313	D₄	—	2	2	no	—
314	D₄	—	14	4	no	—
315	D₄	—	14	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	7	1	no	—
318	C₂×C₄	—	7	4	no	—
319	C₂×C₄	—	7	2	no	—
320	C₂×C₄	—	7	1	no	—
321	C₂×C₄	—	7	2	no	—
322	C₂×C₄	—	14	2	no	—
323	C₂×C₄	—	14	2	no	—
324	C₂×C₄	—	14	2	no	—
325	C₂×C₄	—	14	4	no	—
326	C₂×C₄	—	14	2	no	—
327	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
328	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
329	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
330	C₇	C₃×#525	1	1	yes	characteristic, complemented, Sylow
331	C₂×C₃	—	7	1	no	—
332	C₂×C₃	—	7	1	no	—
333	C₂×C₃	—	7	1	no	—
334	C₂×C₃	—	14	2	no	—
335	C₂×C₃	—	14	2	no	—
336	C₂×C₃	—	14	2	no	—
337	C₂×C₃	—	28	2	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	7	2	no	—
344	C₂²	—	7	2	no	—
345	C₂²	—	14	8	no	—
346	C₂²	—	14	1	no	—
347	C₂²	—	14	1	no	—
348	C₂²	—	14	1	no	—
349	C₂²	—	14	1	no	—
350	C₂²	#1159⋊C₃	1	2	yes	complemented
351	C₂²	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	—	7	2	no	—
355	C₄	—	14	1	no	—
356	C₄	—	14	2	no	—
357	C₄	—	14	2	no	—
358	C₄	D₄×AGL(1,𝔽₇)	1	2	yes	—
359	C₃	—	7	1	no	Sylow
360	C₂	—	2	2	no	—
361	C₂	—	4	2	no	—
362	C₂	—	14	2	no	—
363	C₂	—	14	2	no	—
364	C₂	C₂×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
365	C₂	C₂×#1159⋊C₃	1	1	yes	characteristic
366	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×#525
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. C₂²×C₄×AGL(1,𝔽₇)	C₂	semidirect
3. ΓL(1,𝔽₈)×#121	C₂	semidirect
4. #6501⋊C₃	C₂	semidirect
5. #6500⋊C₃	C₂	semidirect
6. D₄×ΓL(1,𝔽₈)⋊C₄	C₂	semidirect
7. #6487⋊C₃	C₂	semidirect
8. #6460⋊C₃	C₂	semidirect
9. #6455⋊C₃	C₂	semidirect
10. #6446⋊C₃	C₂	semidirect
11. ((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	semidirect
12. #90297	C₃	semidirect
15. C₂×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
20. C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
27. C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	semidirect
28. C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
29. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
31. (C₂²⋊Dic₇)⋊C₃	C₂²	semidirect
34. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	semidirect
35. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	semidirect
36. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	semidirect
37. C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
38. C₂×#1159	C₂×C₃	semidirect
39. C₂²×C₄×D₇	C₂×C₃	semidirect
40. C₇×#121	C₂×C₃	semidirect
41. #6501	C₂×C₃	semidirect
42. #6500	C₂×C₃	semidirect
43. D₄×Dic₇	C₂×C₃	semidirect
44. #6487	C₂×C₃	semidirect
45. #6460	C₂×C₃	semidirect
46. #6455	C₂×C₃	semidirect
47. #6446	C₂×C₃	semidirect
48. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
74. C₄×AGL(1,𝔽₇)	D₄	semidirect
78. C₂×C₇×D₄	C₂²×C₃	semidirect
83. C₂²×Dic₇	C₂²×C₃	semidirect
90. C₂×Dic₁₄	C₂²×C₃	semidirect
91. C₇×C₄⋊C₄	C₂²×C₃	semidirect
92. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
94. C₂²⋊Dic₇	C₂²×C₃	semidirect
97. C₄⋊Dic₇	C₂²×C₃	semidirect
98. C₄⋊Dic₇	C₂²×C₃	semidirect
99. Dic₇⋊C₄	C₂²×C₃	semidirect
100. C₄×Dic₇	C₂²×C₃	semidirect
117. C₂²×ΓL(1,𝔽₈)	#41	semidirect
125. C₂×AGL(1,𝔽₇)	#41	semidirect
158. C₄×D₇	C₃×D₄	semidirect
198. #121	AGL(1,𝔽₇)	semidirect
208. C₂²×C₇	C₃×#41	semidirect
216. C₂×D₇	C₃×#41	semidirect
250. ΓL(1,𝔽₈)	#525	semidirect
257. C₂×D₄	C₂×AGL(1,𝔽₇)	semidirect
269. C₄⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
274. C₂²⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
330. C₇	C₃×#525	semidirect
350. C₂²	#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
C₂²×C₄×AGL(1,𝔽₇)	2
ΓL(1,𝔽₈)×#121	2
#6501⋊C₃	2
#6500⋊C₃	2
D₄×ΓL(1,𝔽₈)⋊C₄	2
#6487⋊C₃	2
#6460⋊C₃	2
#6455⋊C₃	2
#6446⋊C₃	2
((C₂²⋊D₇)⋊C₃)⋊C₄	2
#90297	3
C₃×#525	7

Subgroups — #90297⋊C3 #13057342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #90297⋊C₃ #13057342