Subgroups — #90303⋊C₃ #13057348

Order 1344.

668 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	C₂×D₄×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#1157⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	#6501⋊C₃	C₂	1	2	yes	maximal, complemented
5	#6500⋊C₃	C₂	1	2	yes	maximal, complemented
6	#6499⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×(C₂²⋊D₇)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#6460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#6456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#6446⋊C₃	C₂	1	2	yes	maximal, complemented
11	C₂²⋊C₄×AGL(1,𝔽₇)	C₂	1	2	yes	maximal, complemented
12	#90303	C₃	1	1	yes	maximal, characteristic, complemented, Hall
13	C₂³×AGL(1,𝔽₇)	C₂²	1	2	yes	—
14	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
15	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
16	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
17	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	—
18	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic
19	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	complemented
20	D₄×AGL(1,𝔽₇)	—	2	4	no	—
21	#1157⋊C₃	—	2	4	no	—
22	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
23	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
24	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
25	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
26	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
28	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
29	(C₂²⋊Dic₇)⋊C₃	C₂²	1	2	yes	complemented
30	(C₂²⋊Dic₇)⋊C₃	C₂²	1	2	yes	complemented
31	(C₂²⋊Dic₇)⋊C₃	C₂²	1	1	yes	characteristic, complemented
32	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic
33	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	—
34	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	complemented
35	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	2	yes	complemented
36	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#1157	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
41	#6501	C₂×C₃	1	2	yes	complemented
42	#6500	C₂×C₃	1	2	yes	complemented
43	#6499	C₂×C₃	1	1	yes	characteristic, complemented
44	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
45	#6460	C₂×C₃	1	1	yes	characteristic, complemented
46	#6456	C₂×C₃	1	1	yes	characteristic, complemented
47	#6446	C₂×C₃	1	2	yes	complemented
48	D₇×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
49	C₃×#546	—	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	4	no	—
53	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
54	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
55	C₂²×AGL(1,𝔽₇)	C₂³	1	2	yes	—
56	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
57	D₄×ΓL(1,𝔽₈)	—	2	2	no	—
58	D₄×ΓL(1,𝔽₈)	—	4	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	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
66	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
67	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
70	C₄⋊AGL(1,𝔽₇)	D₄	1	4	yes	complemented
71	C₄×AGL(1,𝔽₇)	—	2	4	no	—
72	C₄×AGL(1,𝔽₇)	—	2	2	no	—
73	C₄×AGL(1,𝔽₇)	—	4	2	no	—
74	ΓL(1,𝔽₈)⋊Q₈	—	2	2	no	—
75	C₂³×D₇	C₂²×C₃	1	2	yes	—
76	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
78	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
80	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
82	D₄×D₇	—	2	4	no	—
83	#1157	—	2	4	no	—
84	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
87	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
88	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
91	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
92	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
93	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
94	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
96	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
97	C₄⋊Dic₇	C₂²×C₃	1	2	yes	complemented
98	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₂×C₃×#41	—	7	1	no	—
101	C₂²×C₃×D₄	—	7	1	no	—
102	C₃×#124	—	7	1	no	—
103	C₃×#123	—	7	2	no	—
104	C₃×C₂²⋊Q₈	—	7	1	no	—
105	C₃×#121	—	7	2	no	—
106	C₃×#121	—	7	1	no	—
107	C₃×#120	—	7	2	no	—
108	C₃×C₄×D₄	—	7	1	no	—
109	C₃×C₄×D₄	—	7	1	no	—
110	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
111	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
112	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
113	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
114	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
115	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
116	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
117	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
118	C₂×AGL(1,𝔽₇)	—	2	1	no	—
119	C₂×AGL(1,𝔽₇)	—	2	2	no	—
120	C₂×AGL(1,𝔽₇)	—	2	2	no	—
121	C₂×AGL(1,𝔽₇)	—	2	1	no	—
122	C₂×AGL(1,𝔽₇)	—	4	8	no	—
123	C₂×AGL(1,𝔽₇)	C₂×D₄	1	4	yes	—
124	C₂×AGL(1,𝔽₇)	#41	1	2	yes	complemented
125	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
126	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
127	C₄×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	—
128	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
129	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
130	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
131	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
132	#546	—	7	1	no	Sylow
133	C₂³×C₇	C₂³×C₃	1	2	yes	—
134	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
135	C₂²×D₇	—	2	4	no	—
136	C₂²×D₇	—	2	4	no	—
137	C₂²×D₇	—	4	2	no	—
138	C₂²×D₇	C₂³×C₃	1	2	yes	—
139	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
140	C₇×D₄	—	2	2	no	—
141	C₇×D₄	—	4	2	no	—
142	C₂×C₄×C₇	—	2	2	no	—
143	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
145	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
146	C₂²⋊D₇	—	2	4	no	—
147	C₂²⋊D₇	—	2	4	no	—
148	C₂²⋊D₇	—	2	2	no	—
149	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
150	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
151	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
152	C₂×Dic₇	C₂³×C₃	1	2	yes	—
153	D₂₈	C₃×D₄	1	4	yes	complemented
154	C₄×D₇	—	2	4	no	—
155	C₄×D₇	—	2	2	no	—
156	C₄×D₇	—	4	2	no	—
157	Dic₁₄	—	2	2	no	—
158	C₂⁴×C₃	—	7	2	no	—
159	C₃×#41	—	14	4	no	—
160	C₂×C₃×Q₈	—	7	1	no	—
161	C₂×C₃×D₄	—	7	1	no	—
162	C₂×C₃×D₄	—	7	1	no	—
163	C₂×C₃×D₄	—	7	2	no	—
164	C₂×C₃×D₄	—	7	2	no	—
165	C₂×C₃×D₄	—	7	1	no	—
166	C₂×C₃×D₄	—	7	2	no	—
167	C₂×C₃×D₄	—	14	4	no	—
168	C₂²×C₃×C₄	—	7	1	no	—
169	C₂²×C₃×C₄	—	7	2	no	—
170	C₂²×C₃×C₄	—	7	2	no	—
171	C₂²×C₃×C₄	—	7	1	no	—
172	C₃×C₄⋊C₄	—	7	1	no	—
173	C₃×C₄⋊C₄	—	7	2	no	—
174	C₃×C₄⋊C₄	—	7	1	no	—
175	C₃×C₂²⋊C₄	—	7	1	no	—
176	C₃×C₂²⋊C₄	—	7	2	no	—
177	C₃×C₂²⋊C₄	—	7	2	no	—
178	C₃×C₂²⋊C₄	—	7	2	no	—
179	C₃×C₂²⋊C₄	—	7	1	no	—
180	C₃×C₂²⋊C₄	—	7	2	no	—
181	C₃×C₂²⋊C₄	—	7	2	no	—
182	C₃×C₄²	—	7	1	no	—
183	C₂×ΓL(1,𝔽₈)	—	4	2	no	—
184	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
185	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
186	C₂×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
187	C₂×ΓL(1,𝔽₈)	H(5,𝔽₂)	1	1	yes	characteristic
188	AGL(1,𝔽₇)	—	2	2	no	—
189	AGL(1,𝔽₇)	—	2	4	no	—
190	C₂×#41	—	7	1	no	—
191	C₂²×D₄	—	7	1	no	—
192	#124	—	7	1	no	—
193	#123	—	7	2	no	—
194	C₂²⋊Q₈	—	7	1	no	—
195	#121	—	7	2	no	—
196	#121	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
197	#120	—	7	2	no	—
198	C₄×D₄	—	7	1	no	—
199	C₄×D₄	—	7	1	no	—
200	C₂×C₂²⋊C₄	—	7	2	no	—
201	C₂²×C₇	—	2	1	no	—
202	C₂²×C₇	—	2	2	no	—
203	C₂²×C₇	—	2	1	no	—
204	C₂²×C₇	—	2	2	no	—
205	C₂²×C₇	—	2	1	no	—
206	C₂²×C₇	—	2	2	no	—
207	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
208	C₂×D₇	—	2	1	no	—
209	C₂×D₇	—	2	2	no	—
210	C₂×D₇	—	2	2	no	—
211	C₂×D₇	—	2	1	no	—
212	C₂×D₇	—	4	8	no	—
213	C₂×D₇	C₂×C₃×D₄	1	4	yes	—
214	C₂×D₇	C₃×#41	1	2	yes	complemented
215	C₄×C₇	—	2	1	no	—
216	C₄×C₇	—	2	2	no	—
217	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
218	Dic₇	—	2	2	no	—
219	Dic₇	—	2	1	no	—
220	Dic₇	—	2	1	no	—
221	Dic₇	—	2	1	no	—
222	C₂³×C₃	—	7	1	no	—
223	C₂³×C₃	—	7	2	no	—
224	C₂³×C₃	—	7	2	no	—
225	C₂³×C₃	—	7	1	no	—
226	C₂³×C₃	—	14	4	no	—
227	C₂³×C₃	—	14	4	no	—
228	C₂³×C₃	—	28	2	no	—
229	C₃×Q₈	—	14	2	no	—
230	C₃×D₄	—	7	4	no	—
231	C₃×D₄	—	14	2	no	—
232	C₃×D₄	—	14	2	no	—
233	C₃×D₄	—	14	4	no	—
234	C₃×D₄	—	14	4	no	—
235	C₃×D₄	—	28	2	no	—
236	C₂×C₃×C₄	—	7	1	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	1	no	—
241	C₂×C₃×C₄	—	7	2	no	—
242	C₂×C₃×C₄	—	7	1	no	—
243	C₂×C₃×C₄	—	14	2	no	—
244	C₂×C₃×C₄	—	14	2	no	—
245	C₂×C₃×C₄	—	14	4	no	—
246	C₂×C₃×C₄	—	28	2	no	—
247	ΓL(1,𝔽₈)	#546	1	1	yes	characteristic, complemented, Hall
248	C₂⁴	—	7	2	no	—
249	#41	—	14	4	no	—
250	C₂×Q₈	—	7	1	no	—
251	C₂×D₄	—	7	1	no	—
252	C₂×D₄	—	7	2	no	—
253	C₂×D₄	—	7	2	no	—
254	C₂×D₄	—	7	1	no	—
255	C₂×D₄	—	14	4	no	—
256	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
257	C₂×D₄	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
258	C₂²×C₄	—	7	2	no	—
259	C₂²×C₄	—	7	1	no	—
260	C₂²×C₄	—	7	2	no	—
261	C₂²×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
262	C₄⋊C₄	—	7	1	no	—
263	C₄⋊C₄	—	7	2	no	—
264	C₄⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
265	C₂²⋊C₄	—	7	2	no	—
266	C₂²⋊C₄	—	7	1	no	—
267	C₂²⋊C₄	—	7	2	no	—
268	C₂²⋊C₄	—	7	1	no	—
269	C₂²⋊C₄	—	7	2	no	—
270	C₂²⋊C₄	—	7	2	no	—
271	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
272	C₄²	—	7	1	no	—
273	C₂×C₇	—	4	2	no	—
274	C₂×C₇	—	4	1	no	—
275	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
276	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
277	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
278	D₇	—	2	2	no	—
279	D₇	—	2	4	no	—
280	C₂²×C₃	—	7	4	no	—
281	C₂²×C₃	—	7	2	no	—
282	C₂²×C₃	—	7	1	no	—
283	C₂²×C₃	—	14	1	no	—
284	C₂²×C₃	—	14	2	no	—
285	C₂²×C₃	—	14	1	no	—
286	C₂²×C₃	—	14	1	no	—
287	C₂²×C₃	—	14	2	no	—
288	C₂²×C₃	—	14	2	no	—
289	C₂²×C₃	—	14	1	no	—
290	C₂²×C₃	—	14	2	no	—
291	C₂²×C₃	—	14	2	no	—
292	C₂²×C₃	—	14	1	no	—
293	C₂²×C₃	—	28	8	no	—
294	C₃×C₄	—	7	2	no	—
295	C₃×C₄	—	14	1	no	—
296	C₃×C₄	—	14	2	no	—
297	C₃×C₄	—	14	1	no	—
298	C₃×C₄	—	14	2	no	—
299	C₃×C₄	—	14	1	no	—
300	C₃×C₄	—	14	1	no	—
301	C₂³	—	7	1	no	—
302	C₂³	—	7	2	no	—
303	C₂³	—	14	4	no	—
304	C₂³	—	14	4	no	—
305	C₂³	—	28	2	no	—
306	C₂³	C₂²×AGL(1,𝔽₇)	1	2	yes	—
307	C₂³	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
308	Q₈	—	14	2	no	—
309	D₄	—	2	2	no	—
310	D₄	—	4	2	no	—
311	D₄	—	7	4	no	—
312	D₄	—	14	4	no	—
313	D₄	—	14	4	no	—
314	D₄	—	14	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	7	1	no	—
317	C₂×C₄	—	7	1	no	—
318	C₂×C₄	—	7	2	no	—
319	C₂×C₄	—	7	1	no	—
320	C₂×C₄	—	14	4	no	—
321	C₂×C₄	—	14	2	no	—
322	C₂×C₄	—	28	2	no	—
323	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
324	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
325	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
326	C₇	C₃×#546	1	1	yes	characteristic, complemented, Sylow
327	C₂×C₃	—	7	1	no	—
328	C₂×C₃	—	7	1	no	—
329	C₂×C₃	—	7	1	no	—
330	C₂×C₃	—	14	2	no	—
331	C₂×C₃	—	14	4	no	—
332	C₂×C₃	—	28	2	no	—
333	C₂×C₃	—	28	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	7	4	no	—
341	C₂²	—	7	2	no	—
342	C₂²	—	14	1	no	—
343	C₂²	—	14	2	no	—
344	C₂²	—	14	1	no	—
345	C₂²	—	14	2	no	—
346	C₂²	—	28	8	no	—
347	C₂²	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	14	1	no	—
351	C₄	—	14	2	no	—
352	C₄	—	14	1	no	—
353	C₄	—	14	1	no	—
354	C₄	D₄×AGL(1,𝔽₇)	1	2	yes	—
355	C₃	—	7	1	no	Sylow
356	C₂	—	4	2	no	—
357	C₂	—	4	1	no	—
358	C₂	—	14	2	no	—
359	C₂	—	14	4	no	—
360	C₂	C₂×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
361	C₂	#6548⋊C₃	1	1	yes	characteristic
362	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×#546
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×D₄×AGL(1,𝔽₇)	C₂	semidirect
2. C₂×#1157⋊C₃	C₂	semidirect
3. ΓL(1,𝔽₈)×#121	C₂	semidirect
4. #6501⋊C₃	C₂	semidirect
5. #6500⋊C₃	C₂	semidirect
6. #6499⋊C₃	C₂	semidirect
7. C₄×(C₂²⋊D₇)⋊C₃	C₂	semidirect
8. #6460⋊C₃	C₂	semidirect
9. #6456⋊C₃	C₂	semidirect
10. #6446⋊C₃	C₂	semidirect
11. C₂²⋊C₄×AGL(1,𝔽₇)	C₂	semidirect
12. #90303	C₃	semidirect
15. C₂×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
16. C₂²×C₄×ΓL(1,𝔽₈)	C₂²	semidirect
19. C₂×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
24. C₂×C₄×AGL(1,𝔽₇)	C₂²	semidirect
25. C₂×C₄×AGL(1,𝔽₇)	C₂²	semidirect
26. C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	semidirect
27. C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
28. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
29. (C₂²⋊Dic₇)⋊C₃	C₂²	semidirect
30. (C₂²⋊Dic₇)⋊C₃	C₂²	semidirect
31. (C₂²⋊Dic₇)⋊C₃	C₂²	semidirect
34. (C₂×AGL(1,𝔽₇))⋊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×D₄×D₇	C₂×C₃	semidirect
39. C₂×#1157	C₂×C₃	semidirect
40. C₇×#121	C₂×C₃	semidirect
41. #6501	C₂×C₃	semidirect
42. #6500	C₂×C₃	semidirect
43. #6499	C₂×C₃	semidirect
44. C₄×C₂²⋊D₇	C₂×C₃	semidirect
45. #6460	C₂×C₃	semidirect
46. #6456	C₂×C₃	semidirect
47. #6446	C₂×C₃	semidirect
48. D₇×C₂²⋊C₄	C₂×C₃	semidirect
70. C₄⋊AGL(1,𝔽₇)	D₄	semidirect
77. C₂×C₇×D₄	C₂²×C₃	semidirect
78. C₂²×C₄×C₇	C₂²×C₃	semidirect
81. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
86. C₂×C₄×D₇	C₂²×C₃	semidirect
87. C₂×C₄×D₇	C₂²×C₃	semidirect
88. C₂×Dic₁₄	C₂²×C₃	semidirect
89. C₇×C₄⋊C₄	C₂²×C₃	semidirect
90. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
91. C₂²⋊Dic₇	C₂²×C₃	semidirect
92. C₂²⋊Dic₇	C₂²×C₃	semidirect
93. C₂²⋊Dic₇	C₂²×C₃	semidirect
96. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
97. C₄⋊Dic₇	C₂²×C₃	semidirect
98. Dic₇⋊C₄	C₂²×C₃	semidirect
99. C₄×Dic₇	C₂²×C₃	semidirect
124. C₂×AGL(1,𝔽₇)	#41	semidirect
153. D₂₈	C₃×D₄	semidirect
196. #121	AGL(1,𝔽₇)	semidirect
214. C₂×D₇	C₃×#41	semidirect
247. ΓL(1,𝔽₈)	#546	semidirect
257. C₂×D₄	C₂×AGL(1,𝔽₇)	semidirect
261. C₂²×C₄	C₂×AGL(1,𝔽₇)	semidirect
264. C₄⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
271. C₂²⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
326. C₇	C₃×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×AGL(1,𝔽₇)	2
C₂×#1157⋊C₃	2
ΓL(1,𝔽₈)×#121	2
#6501⋊C₃	2
#6500⋊C₃	2
#6499⋊C₃	2
C₄×(C₂²⋊D₇)⋊C₃	2
#6460⋊C₃	2
#6456⋊C₃	2
#6446⋊C₃	2
C₂²⋊C₄×AGL(1,𝔽₇)	2
#90303	3
C₃×#546	7

Subgroups — #90303⋊C3 #13057348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #90303⋊C₃ #13057348