Subgroups — D₄×C₄⋊AGL(1,𝔽₇) #13057286

Order 1344.

856 conjugacy classes of subgroups.

The subgroup lattice has 280 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	2	yes	maximal, complemented
2	C₂²×C₄⋊AGL(1,𝔽₇)	C₂	1	2	yes	maximal, complemented
3	C₄×D₄×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#6493⋊C₃	C₂	1	2	yes	maximal, complemented
5	#6458⋊C₃	C₂	1	2	yes	maximal, complemented
6	#6445⋊C₃	C₂	1	4	yes	maximal, complemented
7	#10620710	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₄⋊AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×D₂₈	C₃	1	1	yes	maximal, characteristic, complemented, Hall
10	C₂³×AGL(1,𝔽₇)	C₂²	1	4	yes	complemented
11	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
12	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
13	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	4	yes	complemented
14	D₄×AGL(1,𝔽₇)	—	2	8	no	—
15	C₂×C₄⋊AGL(1,𝔽₇)	—	2	8	no	—
16	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
18	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
19	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	4	yes	complemented
20	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
21	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
22	C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
23	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
24	C₄²×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
25	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	complemented
26	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	4	yes	complemented
27	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₄×D₇	C₂×C₃	1	2	yes	complemented
29	C₂²×D₂₈	C₂×C₃	1	2	yes	complemented
30	C₄×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
31	#6493	C₂×C₃	1	2	yes	complemented
32	#6458	C₂×C₃	1	2	yes	complemented
33	#6445	C₂×C₃	1	4	yes	complemented
34	#6437	C₂×C₃	1	1	yes	characteristic, complemented
35	C₄×D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
36	C₃×D₄²	—	7	1	no	maximal, Hall
37	C₂³×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
38	C₂²×AGL(1,𝔽₇)	—	2	8	no	—
39	C₂²×AGL(1,𝔽₇)	—	2	8	no	—
40	C₂²×AGL(1,𝔽₇)	—	4	4	no	—
41	C₂²×AGL(1,𝔽₇)	C₂³	1	4	yes	—
42	C₂²×AGL(1,𝔽₇)	C₂³	1	2	yes	—
43	D₄×ΓL(1,𝔽₈)	D₄	1	4	yes	complemented
44	C₂×C₄×ΓL(1,𝔽₈)	—	2	4	no	—
45	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
46	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
47	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
48	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
49	(C₂²⋊D₇)⋊C₃	—	2	8	no	—
50	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
51	C₄⋊AGL(1,𝔽₇)	—	2	8	no	—
52	C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
53	C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
54	C₄⋊AGL(1,𝔽₇)	—	4	2	no	—
55	C₄⋊AGL(1,𝔽₇)	D₄	1	4	yes	direct product factor
56	C₄×AGL(1,𝔽₇)	—	2	4	no	—
57	C₂³×D₇	C₂²×C₃	1	4	yes	complemented
58	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
59	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	complemented
60	C₂×C₂²⋊D₇	C₂²×C₃	1	4	yes	complemented
61	D₄×D₇	—	2	8	no	—
62	C₂×D₂₈	—	2	8	no	—
63	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
64	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
65	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
66	C₂×D₂₈	C₂²×C₃	1	4	yes	complemented
67	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
68	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
69	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
70	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
71	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
72	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
73	(C₂×D₇)⋊C₄	C₂²×C₃	1	4	yes	complemented
74	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
75	C₂²×C₃×D₄	—	7	2	no	—
76	C₂²×C₃×D₄	—	7	2	no	—
77	C₃×#127	—	7	1	no	—
78	C₃×#121	—	7	2	no	—
79	C₃×#121	—	7	2	no	—
80	C₃×#120	—	7	4	no	—
81	C₃×C₄×D₄	—	7	1	no	—
82	C₃×C₄×D₄	—	7	1	no	—
83	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
84	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
85	C₂²×ΓL(1,𝔽₈)	C₂×D₄	1	4	yes	complemented
86	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
87	C₂×AGL(1,𝔽₇)	—	2	2	no	—
88	C₂×AGL(1,𝔽₇)	—	2	2	no	—
89	C₂×AGL(1,𝔽₇)	—	2	4	no	—
90	C₂×AGL(1,𝔽₇)	—	2	4	no	—
91	C₂×AGL(1,𝔽₇)	—	2	4	no	—
92	C₂×AGL(1,𝔽₇)	—	4	16	no	—
93	C₂×AGL(1,𝔽₇)	C₂×D₄	1	4	yes	complemented
94	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
95	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
96	C₄×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	complemented
97	C₄×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	complemented
98	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
99	D₄²	—	7	1	no	Sylow
100	C₂³×C₇	C₂³×C₃	1	2	yes	—
101	C₂²×D₇	—	2	8	no	—
102	C₂²×D₇	—	2	8	no	—
103	C₂²×D₇	—	4	4	no	—
104	C₂²×D₇	C₂³×C₃	1	4	yes	—
105	C₂²×D₇	C₂³×C₃	1	2	yes	—
106	C₇×D₄	C₃×D₄	1	4	yes	complemented
107	C₂×C₄×C₇	—	2	4	no	—
108	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
109	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
110	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
111	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
112	C₂²⋊D₇	—	2	8	no	—
113	C₂×Dic₇	C₂³×C₃	1	2	yes	—
114	D₂₈	—	2	8	no	—
115	D₂₈	—	2	4	no	—
116	D₂₈	—	2	4	no	—
117	D₂₈	—	4	2	no	—
118	D₂₈	C₃×D₄	1	4	yes	complemented
119	C₄×D₇	—	2	4	no	—
120	C₂⁴×C₃	—	7	4	no	—
121	C₂×C₃×D₄	—	7	1	no	—
122	C₂×C₃×D₄	—	7	4	no	—
123	C₂×C₃×D₄	—	7	2	no	—
124	C₂×C₃×D₄	—	7	2	no	—
125	C₂×C₃×D₄	—	7	4	no	—
126	C₂×C₃×D₄	—	7	2	no	—
127	C₂×C₃×D₄	—	7	1	no	—
128	C₂×C₃×D₄	—	14	8	no	—
129	C₂×C₃×D₄	—	14	8	no	—
130	C₂²×C₃×C₄	—	7	2	no	—
131	C₂²×C₃×C₄	—	7	2	no	—
132	C₃×C₄⋊C₄	—	7	1	no	—
133	C₃×C₄⋊C₄	—	7	1	no	—
134	C₃×C₂²⋊C₄	—	7	2	no	—
135	C₃×C₂²⋊C₄	—	7	4	no	—
136	C₃×C₂²⋊C₄	—	7	2	no	—
137	C₃×C₄²	—	7	1	no	—
138	C₂×ΓL(1,𝔽₈)	—	2	4	no	—
139	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
140	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
141	C₂×ΓL(1,𝔽₈)	H(5,𝔽₂)	1	1	yes	characteristic
142	AGL(1,𝔽₇)	—	2	4	no	—
143	AGL(1,𝔽₇)	—	4	4	no	—
144	C₂²×D₄	—	7	2	no	—
145	C₂²×D₄	—	7	2	no	—
146	#127	—	7	1	no	—
147	#121	—	7	2	no	—
148	#121	—	7	2	no	—
149	#120	—	7	4	no	—
150	C₄×D₄	—	7	1	no	—
151	C₄×D₄	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
152	C₂²×C₇	—	2	2	no	—
153	C₂²×C₇	—	2	2	no	—
154	C₂²×C₇	C₂×C₃×D₄	1	4	yes	complemented
155	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
156	C₂×D₇	—	2	2	no	—
157	C₂×D₇	—	2	2	no	—
158	C₂×D₇	—	2	4	no	—
159	C₂×D₇	—	2	4	no	—
160	C₂×D₇	—	2	4	no	—
161	C₂×D₇	—	4	16	no	—
162	C₂×D₇	C₂×C₃×D₄	1	4	yes	complemented
163	C₄×C₇	—	2	2	no	—
164	C₄×C₇	—	2	1	no	—
165	C₄×C₇	C₂×C₃×D₄	1	2	yes	complemented
166	C₄×C₇	C₂×C₃×D₄	1	2	yes	complemented
167	Dic₇	—	2	2	no	—
168	C₂³×C₃	—	7	2	no	—
169	C₂³×C₃	—	7	4	no	—
170	C₂³×C₃	—	7	2	no	—
171	C₂³×C₃	—	14	8	no	—
172	C₂³×C₃	—	14	8	no	—
173	C₂³×C₃	—	28	4	no	—
174	C₃×D₄	—	7	4	no	—
175	C₃×D₄	—	7	4	no	—
176	C₃×D₄	—	14	4	no	—
177	C₃×D₄	—	14	4	no	—
178	C₃×D₄	—	14	8	no	—
179	C₃×D₄	—	14	8	no	—
180	C₃×D₄	—	28	2	no	—
181	C₂×C₃×C₄	—	7	2	no	—
182	C₂×C₃×C₄	—	7	1	no	—
183	C₂×C₃×C₄	—	7	1	no	—
184	C₂×C₃×C₄	—	7	1	no	—
185	C₂×C₃×C₄	—	7	2	no	—
186	C₂×C₃×C₄	—	14	4	no	—
187	C₂×C₃×C₄	—	14	4	no	—
188	ΓL(1,𝔽₈)	D₄²	1	1	yes	characteristic, complemented, Hall
189	C₂⁴	—	7	4	no	—
190	C₂×D₄	—	7	4	no	—
191	C₂×D₄	—	7	1	no	—
192	C₂×D₄	—	7	4	no	—
193	C₂×D₄	—	7	2	no	—
194	C₂×D₄	—	7	2	no	—
195	C₂×D₄	—	7	2	no	—
196	C₂×D₄	—	14	8	no	—
197	C₂×D₄	—	14	8	no	—
198	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
199	C₂²×C₄	—	7	2	no	—
200	C₂²×C₄	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
201	C₄⋊C₄	—	7	1	no	—
202	C₄⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
203	C₂²⋊C₄	—	7	2	no	—
204	C₂²⋊C₄	—	7	4	no	—
205	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
206	C₄²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
207	C₂×C₇	—	2	4	no	—
208	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
209	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
210	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
211	D₇	—	2	4	no	—
212	D₇	—	4	4	no	—
213	C₂²×C₃	—	7	4	no	—
214	C₂²×C₃	—	7	4	no	—
215	C₂²×C₃	—	7	1	no	—
216	C₂²×C₃	—	14	2	no	—
217	C₂²×C₃	—	14	2	no	—
218	C₂²×C₃	—	14	2	no	—
219	C₂²×C₃	—	14	2	no	—
220	C₂²×C₃	—	14	4	no	—
221	C₂²×C₃	—	14	4	no	—
222	C₂²×C₃	—	14	4	no	—
223	C₂²×C₃	—	28	16	no	—
224	C₃×C₄	—	7	2	no	—
225	C₃×C₄	—	7	2	no	—
226	C₃×C₄	—	14	2	no	—
227	C₃×C₄	—	14	1	no	—
228	C₃×C₄	—	14	2	no	—
229	C₂³	—	7	2	no	—
230	C₂³	—	7	4	no	—
231	C₂³	—	14	8	no	—
232	C₂³	—	14	8	no	—
233	C₂³	—	28	4	no	—
234	C₂³	C₂²×AGL(1,𝔽₇)	1	2	yes	—
235	D₄	—	7	4	no	—
236	D₄	—	14	8	no	—
237	D₄	—	14	8	no	—
238	D₄	—	14	4	no	—
239	D₄	—	14	4	no	—
240	D₄	—	28	2	no	—
241	D₄	C₄⋊AGL(1,𝔽₇)	1	4	yes	direct product factor
242	C₂×C₄	—	2	4	no	—
243	C₂×C₄	—	7	2	no	—
244	C₂×C₄	—	14	4	no	—
245	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
246	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
247	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
248	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
249	C₇	C₃×D₄²	1	1	yes	characteristic, complemented, Sylow
250	C₂×C₃	—	7	1	no	—
251	C₂×C₃	—	7	1	no	—
252	C₂×C₃	—	7	1	no	—
253	C₂×C₃	—	14	4	no	—
254	C₂×C₃	—	14	4	no	—
255	C₂×C₃	—	28	4	no	—
256	C₂²	—	2	2	no	—
257	C₂²	—	2	2	no	—
258	C₂²	—	7	4	no	—
259	C₂²	—	14	2	no	—
260	C₂²	—	14	2	no	—
261	C₂²	—	14	4	no	—
262	C₂²	—	14	4	no	—
263	C₂²	—	14	4	no	—
264	C₂²	—	28	16	no	—
265	C₂²	C₂×C₄⋊AGL(1,𝔽₇)	1	4	yes	complemented
266	C₂²	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
267	C₄	—	2	2	no	—
268	C₄	—	2	1	no	—
269	C₄	—	14	2	no	—
270	C₄	C₂×C₄⋊AGL(1,𝔽₇)	1	2	yes	complemented
271	C₄	D₄×AGL(1,𝔽₇)	1	2	yes	complemented
272	C₃	—	7	1	no	Sylow
273	C₂	—	2	4	no	—
274	C₂	—	14	4	no	—
275	C₂	—	28	4	no	—
276	C₂	C₂²×C₄⋊AGL(1,𝔽₇)	1	1	yes	characteristic
277	C₂	C₂×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
278	C₂	#10621518	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₇	C₂⁴×C₃
Fitting	C₄×C₇×D₄	C₂×C₃
hypercenter	C₄×D₄	AGL(1,𝔽₇)
hypocenter	C₇	C₃×D₄²
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄

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. C₂²×C₄⋊AGL(1,𝔽₇)	C₂	semidirect
3. C₄×D₄×ΓL(1,𝔽₈)	C₂	semidirect
4. #6493⋊C₃	C₂	semidirect
5. #6458⋊C₃	C₂	semidirect
6. #6445⋊C₃	C₂	semidirect
7. #10620710	C₂	semidirect
8. C₄×C₄⋊AGL(1,𝔽₇)	C₂	semidirect
9. D₄×D₂₈	C₃	semidirect
10. C₂³×AGL(1,𝔽₇)	C₂²	semidirect
12. C₂²×C₄×ΓL(1,𝔽₈)	C₂²	semidirect
13. C₂×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
17. C₂×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
18. C₂×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
19. C₂×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
20. C₂×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
21. C₂×C₄×AGL(1,𝔽₇)	C₂²	semidirect
22. C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
23. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
24. C₄²×ΓL(1,𝔽₈)	C₂²	semidirect
25. (C₂×AGL(1,𝔽₇))⋊C₄	C₂²	semidirect
26. (C₂×AGL(1,𝔽₇))⋊C₄	C₂²	semidirect
27. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	semidirect
28. C₂×D₄×D₇	C₂×C₃	semidirect
29. C₂²×D₂₈	C₂×C₃	semidirect
30. C₄×C₇×D₄	C₂×C₃	semidirect
31. #6493	C₂×C₃	semidirect
32. #6458	C₂×C₃	semidirect
33. #6445	C₂×C₃	semidirect
34. #6437	C₂×C₃	semidirect
35. C₄×D₂₈	C₂×C₃	semidirect
43. D₄×ΓL(1,𝔽₈)	D₄	semidirect
55. C₄⋊AGL(1,𝔽₇)	D₄	direct (N × H)
57. C₂³×D₇	C₂²×C₃	semidirect
59. C₂²×C₄×C₇	C₂²×C₃	semidirect
60. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
64. C₂×D₂₈	C₂²×C₃	semidirect
65. C₂×D₂₈	C₂²×C₃	semidirect
66. C₂×D₂₈	C₂²×C₃	semidirect
67. C₂×D₂₈	C₂²×C₃	semidirect
68. C₂×C₄×D₇	C₂²×C₃	semidirect
69. C₇×C₄⋊C₄	C₂²×C₃	semidirect
70. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
71. C₄²×C₇	C₂²×C₃	semidirect
72. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
73. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
74. C₄⋊Dic₇	C₂²×C₃	semidirect
85. C₂²×ΓL(1,𝔽₈)	C₂×D₄	semidirect
93. C₂×AGL(1,𝔽₇)	C₂×D₄	semidirect
96. C₄×ΓL(1,𝔽₈)	C₂×D₄	semidirect
97. C₄×ΓL(1,𝔽₈)	C₂×D₄	semidirect
106. C₇×D₄	C₃×D₄	semidirect
118. D₂₈	C₃×D₄	semidirect
151. C₄×D₄	AGL(1,𝔽₇)	semidirect
154. C₂²×C₇	C₂×C₃×D₄	semidirect
162. C₂×D₇	C₂×C₃×D₄	semidirect
165. C₄×C₇	C₂×C₃×D₄	semidirect
166. C₄×C₇	C₂×C₃×D₄	semidirect
188. ΓL(1,𝔽₈)	D₄²	semidirect
200. C₂²×C₄	C₂×AGL(1,𝔽₇)	semidirect
202. C₄⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
205. C₂²⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
206. C₄²	C₂×AGL(1,𝔽₇)	semidirect
241. D₄	C₄⋊AGL(1,𝔽₇)	direct (N × H)
249. C₇	C₃×D₄²	semidirect
265. C₂²	C₂×C₄⋊AGL(1,𝔽₇)	semidirect
270. C₄	C₂×C₄⋊AGL(1,𝔽₇)	semidirect
271. C₄	D₄×AGL(1,𝔽₇)	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
C₂²×C₄⋊AGL(1,𝔽₇)	2
C₄×D₄×ΓL(1,𝔽₈)	2
#6493⋊C₃	2
#6458⋊C₃	2
#6445⋊C₃	2
#10620710	2
C₄×C₄⋊AGL(1,𝔽₇)	2
D₄×D₂₈	3
C₃×D₄²	7

Subgroups — D4×C4⋊AGL(1,𝔽7) #13057286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₄⋊AGL(1,𝔽₇) #13057286