Subgroups — C₂×D₁₂×AGL(1,𝔽₇) #72244121

Order 2016.

998 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×AGL(1,𝔽₇)	C₂	1	2	yes	maximal, complemented
2	C₂×C₄⋊(C₃⋊AGL(1,𝔽₇))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×ΓL(1,𝔽₈)×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#4247⋊C₃	C₂	1	2	yes	maximal, complemented
6	D₁₂×AGL(1,𝔽₇)	C₂	1	8	yes	maximal, direct product factor
7	C₂×D₇×D₁₂	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×AGL(1,𝔽₇)	—	3	1	no	maximal
9	C₂²×C₃⋊AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
10	C₂²×D₃×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
11	C₂²×C₃×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
12	C₂×D₃×AGL(1,𝔽₇)	—	2	8	no	—
13	C₂×D₃×AGL(1,𝔽₇)	C₂²	1	8	yes	complemented
14	C₂×C₃×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
15	C₄⋊(C₃⋊AGL(1,𝔽₇))	C₂²	1	4	yes	complemented
16	ΓL(1,𝔽₈)×D₁₂	C₂²	1	4	yes	complemented
17	C₂×C₃×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₄×AGL(1,𝔽₇)	C₂²	1	4	yes	complemented
19	#4247⋊C₃	C₂²	1	8	yes	complemented
20	C₂²×D₃×D₇	C₂×C₃	1	2	yes	complemented
21	C₂³×AGL(1,𝔽₇)	—	3	2	no	—
22	C₂×D₈₄	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂×C₇×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₃×C₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×D₄×ΓL(1,𝔽₈)	—	3	1	no	—
26	C₂×#4247	C₂×C₃	1	2	yes	complemented
27	D₇×D₁₂	C₂×C₃	1	8	yes	complemented
28	C₂×(C₂²⋊D₇)⋊C₃	—	3	2	no	—
29	D₄×AGL(1,𝔽₇)	—	3	8	no	—
30	C₂×C₄⋊AGL(1,𝔽₇)	—	3	1	no	—
31	C₂×C₄×AGL(1,𝔽₇)	—	2	1	no	—
32	C₂×C₄×AGL(1,𝔽₇)	D₃	1	1	yes	characteristic, complemented
33	C₂²×C₃×D₁₂	—	7	1	no	maximal, Hall
34	C₂²×C₃×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
35	C₂×C₃⋊AGL(1,𝔽₇)	—	2	4	no	—
36	C₂×C₃⋊AGL(1,𝔽₇)	C₂³	1	4	yes	complemented
37	C₂×D₃×ΓL(1,𝔽₈)	—	2	4	no	—
38	C₂×D₃×ΓL(1,𝔽₈)	C₂³	1	4	yes	complemented
39	C₂×C₃×AGL(1,𝔽₇)	D₄	1	4	yes	complemented
40	C₂×C₃×AGL(1,𝔽₇)	C₂³	1	2	yes	—
41	D₃×AGL(1,𝔽₇)	—	2	16	no	—
42	C₃×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
43	C₃×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	complemented
44	C₂×D₄×D₇	—	3	1	no	Hall
45	C₂²×D₂₁	C₂²×C₃	1	2	yes	complemented
46	C₂²×D₃×C₇	C₂²×C₃	1	2	yes	complemented
47	C₂²×C₃×D₇	C₂²×C₃	1	1	yes	characteristic
48	C₂³×ΓL(1,𝔽₈)	—	3	2	no	—
49	C₂×D₃×D₇	—	2	8	no	—
50	C₂×D₃×D₇	C₂²×C₃	1	8	yes	complemented
51	C₂²×AGL(1,𝔽₇)	—	2	1	no	—
52	C₂²×AGL(1,𝔽₇)	—	3	2	no	—
53	C₂²×AGL(1,𝔽₇)	—	3	8	no	—
54	C₂²×AGL(1,𝔽₇)	—	6	8	no	—
55	C₂²×AGL(1,𝔽₇)	C₂×D₃	1	1	yes	characteristic
56	C₂×C₃×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
57	D₈₄	C₂²×C₃	1	4	yes	complemented
58	C₇×D₁₂	C₂²×C₃	1	4	yes	complemented
59	C₂×C₃×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
60	C₃×C₄×D₇	C₂²×C₃	1	4	yes	complemented
61	D₄×ΓL(1,𝔽₈)	—	3	4	no	—
62	C₂×C₄×ΓL(1,𝔽₈)	—	2	1	no	—
63	C₂×C₄×ΓL(1,𝔽₈)	C₂×D₃	1	1	yes	characteristic, complemented
64	#4247	C₂²×C₃	1	8	yes	complemented
65	(C₂²⋊D₇)⋊C₃	—	3	8	no	—
66	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
67	C₂×ΓL(1,𝔽₈)⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
68	C₄⋊AGL(1,𝔽₇)	—	3	4	no	—
69	C₄×AGL(1,𝔽₇)	—	2	4	no	—
70	C₄×AGL(1,𝔽₇)	C₂×D₃	1	4	yes	complemented
71	C₂³×C₃×D₃	—	7	2	no	—
72	C₂²×C₃²×C₄	—	7	1	no	—
73	C₂×C₃×D₁₂	—	7	2	no	—
74	C₂×C₃×D₁₂	—	7	1	no	—
75	C₂×C₃×D₁₂	—	7	8	no	—
76	C₂×C₃×D₁₂	—	14	1	no	—
77	C₂×C₃×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	complemented
78	C₂×C₃×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
79	C₃⋊AGL(1,𝔽₇)	—	2	4	no	—
80	D₃×ΓL(1,𝔽₈)	—	2	4	no	—
81	C₃×AGL(1,𝔽₇)	C₂×D₄	1	4	yes	complemented
82	C₂³×D₇	—	3	2	no	—
83	C₂×C₇×D₄	—	3	1	no	—
84	C₂×C₂²⋊D₇	—	3	2	no	—
85	D₄×D₇	—	3	8	no	—
86	C₂×D₂₈	—	3	1	no	—
87	C₂×C₄×D₇	C₃×D₃	1	1	yes	characteristic, complemented
88	C₂²×C₃×D₄	—	21	1	no	—
89	C₂²×D₁₂	—	7	1	no	—
90	C₂²×C₃×C₇	C₂³×C₃	1	1	yes	characteristic
91	C₂×D₂₁	—	2	4	no	—
92	C₂×D₂₁	C₂³×C₃	1	4	yes	complemented
93	C₂×D₃×C₇	—	2	4	no	—
94	C₂×D₃×C₇	C₂³×C₃	1	4	yes	complemented
95	C₂×C₃×D₇	C₃×D₄	1	4	yes	complemented
96	C₂×C₃×D₇	C₂³×C₃	1	2	yes	—
97	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
98	C₂²×ΓL(1,𝔽₈)	—	3	4	no	—
99	C₂²×ΓL(1,𝔽₈)	—	6	4	no	—
100	C₂²×ΓL(1,𝔽₈)	C₂²×D₃	1	1	yes	characteristic
101	D₃×D₇	—	2	16	no	—
102	C₂×AGL(1,𝔽₇)	—	2	4	no	—
103	C₂×AGL(1,𝔽₇)	—	2	2	no	—
104	C₂×AGL(1,𝔽₇)	—	3	4	no	—
105	C₂×AGL(1,𝔽₇)	—	6	4	no	—
106	C₂×AGL(1,𝔽₇)	—	6	16	no	—
107	C₂×AGL(1,𝔽₇)	D₁₂	1	4	yes	direct product factor
108	C₂×AGL(1,𝔽₇)	C₂²×D₃	1	2	yes	—
109	C₃×C₄×C₇	C₂³×C₃	1	2	yes	complemented
110	C₃×Dic₇	C₂³×C₃	1	2	yes	complemented
111	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
112	C₄×ΓL(1,𝔽₈)	C₂²×D₃	1	2	yes	complemented
113	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
114	ΓL(1,𝔽₈)⋊C₄	C₂²×D₃	1	2	yes	complemented
115	C₂³×C₃²	—	7	1	no	—
116	C₂²×C₃×D₃	—	7	2	no	—
117	C₂²×C₃×D₃	—	7	8	no	—
118	C₂²×C₃×D₃	—	14	8	no	—
119	C₂²×C₃×D₃	—	14	2	no	—
120	C₂×C₃²×C₄	—	7	1	no	—
121	C₂×C₃²×C₄	—	7	4	no	—
122	C₂×C₃²×C₄	—	14	1	no	—
123	C₃×D₁₂	—	7	8	no	—
124	C₃×D₁₂	—	7	4	no	—
125	C₃×D₁₂	—	14	4	no	—
126	C₃×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
127	C₂³×C₇	—	3	2	no	—
128	C₂²×D₇	—	3	2	no	—
129	C₂²×D₇	—	3	8	no	—
130	C₂²×D₇	—	6	8	no	—
131	C₂²×D₇	C₂×C₃×D₃	1	1	yes	characteristic
132	C₇×D₄	—	3	4	no	—
133	C₂×C₄×C₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented
134	C₂²⋊D₇	—	3	8	no	—
135	C₂×Dic₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented
136	D₂₈	—	3	4	no	—
137	C₄×D₇	C₂×C₃×D₃	1	4	yes	complemented
138	C₂⁴×C₃	—	21	2	no	—
139	C₂³×D₃	—	7	2	no	—
140	C₂×C₃×D₄	—	21	2	no	—
141	C₂×C₃×D₄	—	21	8	no	—
142	C₂×C₃×D₄	—	21	1	no	—
143	C₂×C₃×D₄	—	42	1	no	—
144	C₂²×C₃×C₄	—	7	1	no	—
145	C₂²×C₃×C₄	—	7	1	no	—
146	C₂²×C₃×C₄	—	14	1	no	—
147	C₂×D₁₂	—	7	2	no	—
148	C₂×D₁₂	—	7	1	no	—
149	C₂×D₁₂	—	7	8	no	—
150	C₂×D₁₂	AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor
151	C₂×C₃×C₇	C₂×C₃×D₄	1	2	yes	complemented
152	C₂×C₃×C₇	C₂⁴×C₃	1	1	yes	characteristic
153	D₂₁	—	2	4	no	—
154	C₃×D₇	C₂×C₃×D₄	1	4	yes	complemented
155	D₃×C₇	—	2	4	no	—
156	C₂×ΓL(1,𝔽₈)	—	2	1	no	—
157	C₂×ΓL(1,𝔽₈)	—	2	2	no	—
158	C₂×ΓL(1,𝔽₈)	—	6	4	no	—
159	C₂×ΓL(1,𝔽₈)	C₂×D₁₂	1	2	yes	complemented
160	C₂×ΓL(1,𝔽₈)	C₂³×D₃	1	1	yes	characteristic
161	AGL(1,𝔽₇)	—	2	4	no	—
162	AGL(1,𝔽₇)	—	6	4	no	—
163	AGL(1,𝔽₇)	C₂×D₁₂	1	4	yes	direct product factor
164	C₂²×C₃²	—	7	4	no	—
165	C₂²×C₃²	—	7	2	no	—
166	C₂²×C₃²	—	14	1	no	—
167	C₂×C₃×D₃	—	7	4	no	—
168	C₂×C₃×D₃	—	14	4	no	—
169	C₂×C₃×D₃	—	14	16	no	—
170	C₂×C₃×D₃	—	14	4	no	—
171	C₂×C₃×D₃	—	28	4	no	—
172	C₃²×C₄	—	7	2	no	—
173	C₃²×C₄	—	14	2	no	—
174	C₂²×D₄	—	21	1	no	Sylow
175	C₂²×C₇	—	3	4	no	—
176	C₂²×C₇	—	6	4	no	—
177	C₂²×C₇	C₂²×C₃×D₃	1	1	yes	characteristic
178	C₂×D₇	—	3	4	no	—
179	C₂×D₇	—	6	4	no	—
180	C₂×D₇	—	6	16	no	—
181	C₂×D₇	C₃×D₁₂	1	4	yes	complemented
182	C₂×D₇	C₂²×C₃×D₃	1	2	yes	—
183	C₄×C₇	C₂²×C₃×D₃	1	2	yes	complemented
184	Dic₇	C₂²×C₃×D₃	1	2	yes	complemented
185	C₂³×C₃	—	7	1	no	—
186	C₂³×C₃	—	7	1	no	—
187	C₂³×C₃	—	14	1	no	—
188	C₂³×C₃	—	21	8	no	—
189	C₂³×C₃	—	21	2	no	—
190	C₂³×C₃	—	42	2	no	—
191	C₂³×C₃	—	42	8	no	—
192	C₂²×D₃	—	7	2	no	—
193	C₂²×D₃	—	7	8	no	—
194	C₂²×D₃	—	14	8	no	—
195	C₂²×D₃	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
196	C₃×D₄	—	21	8	no	—
197	C₃×D₄	—	21	4	no	—
198	C₃×D₄	—	42	4	no	—
199	C₂×C₃×C₄	—	7	1	no	—
200	C₂×C₃×C₄	—	7	1	no	—
201	C₂×C₃×C₄	—	7	4	no	—
202	C₂×C₃×C₄	—	7	4	no	—
203	C₂×C₃×C₄	—	14	1	no	—
204	C₂×C₃×C₄	—	14	4	no	—
205	C₂×C₃×C₄	—	14	1	no	—
206	C₂×C₃×C₄	—	28	1	no	—
207	C₂×C₃×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
208	D₁₂	—	7	8	no	—
209	D₁₂	—	7	4	no	—
210	D₁₂	C₂×AGL(1,𝔽₇)	1	4	yes	direct product factor
211	C₃×C₇	C₂²×C₃×D₄	1	1	yes	characteristic, complemented
212	ΓL(1,𝔽₈)	—	2	1	no	—
213	ΓL(1,𝔽₈)	C₂²×D₁₂	1	1	yes	characteristic, complemented
214	C₂×C₃²	—	7	4	no	—
215	C₂×C₃²	—	14	2	no	—
216	C₂×C₃²	—	14	1	no	—
217	C₃×D₃	—	14	4	no	—
218	C₃×D₃	—	28	4	no	—
219	C₂⁴	—	21	2	no	—
220	C₂×D₄	—	3	1	no	—
221	C₂×D₄	—	21	8	no	—
222	C₂×D₄	—	21	2	no	—
223	C₂×D₄	—	21	1	no	—
224	C₂²×C₄	—	7	1	no	—
225	C₂×C₇	—	6	4	no	—
226	C₂×C₇	C₂×C₃×D₁₂	1	2	yes	complemented
227	C₂×C₇	C₂³×C₃×D₃	1	1	yes	characteristic
228	D₇	—	6	4	no	—
229	D₇	C₂×C₃×D₁₂	1	4	yes	complemented
230	C₂²×C₃	—	7	2	no	—
231	C₂²×C₃	—	7	4	no	—
232	C₂²×C₃	—	7	4	no	—
233	C₂²×C₃	—	7	2	no	—
234	C₂²×C₃	—	14	2	no	—
235	C₂²×C₃	—	14	4	no	—
236	C₂²×C₃	—	14	1	no	—
237	C₂²×C₃	—	21	4	no	—
238	C₂²×C₃	—	28	1	no	—
239	C₂²×C₃	—	42	4	no	—
240	C₂²×C₃	—	42	16	no	—
241	C₂²×C₃	—	42	4	no	—
242	C₂²×C₃	—	84	4	no	—
243	C₂²×C₃	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
244	C₂×D₃	—	2	4	no	—
245	C₂×D₃	—	7	4	no	—
246	C₂×D₃	—	14	16	no	—
247	C₂×D₃	—	14	4	no	—
248	C₂×D₃	C₂²×AGL(1,𝔽₇)	1	4	yes	complemented
249	C₃×C₄	—	7	2	no	—
250	C₃×C₄	—	7	2	no	—
251	C₃×C₄	—	14	2	no	—
252	C₃×C₄	—	14	2	no	—
253	C₃×C₄	—	28	2	no	—
254	C₃×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
255	C₃²	—	14	1	no	Sylow
256	C₂³	—	3	2	no	—
257	C₂³	—	7	1	no	—
258	C₂³	—	21	8	no	—
259	C₂³	—	21	2	no	—
260	C₂³	—	42	8	no	—
261	D₄	—	3	4	no	—
262	D₄	—	21	8	no	—
263	D₄	—	21	4	no	—
264	C₂×C₄	—	7	1	no	—
265	C₂×C₄	—	7	4	no	—
266	C₂×C₄	D₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
267	C₇	C₂²×C₃×D₁₂	1	1	yes	characteristic, complemented, Sylow
268	C₂×C₃	—	7	4	no	—
269	C₂×C₃	—	7	4	no	—
270	C₂×C₃	—	14	4	no	—
271	C₂×C₃	—	14	2	no	—
272	C₂×C₃	—	14	1	no	—
273	C₂×C₃	—	28	2	no	—
274	C₂×C₃	—	28	1	no	—
275	C₂×C₃	—	42	4	no	—
276	C₂×C₃	—	84	4	no	—
277	C₂×C₃	D₄×AGL(1,𝔽₇)	1	2	yes	complemented
278	C₂×C₃	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
279	D₃	—	2	4	no	—
280	D₃	—	14	4	no	—
281	C₂²	—	3	4	no	—
282	C₂²	—	6	4	no	—
283	C₂²	—	7	4	no	—
284	C₂²	—	7	2	no	—
285	C₂²	—	21	4	no	—
286	C₂²	—	42	16	no	—
287	C₂²	—	42	4	no	—
288	C₂²	C₂×D₃×AGL(1,𝔽₇)	1	1	yes	characteristic
289	C₄	—	7	2	no	—
290	C₄	C₂×D₃×AGL(1,𝔽₇)	1	2	yes	complemented
291	C₃	—	14	1	no	—
292	C₃	—	28	1	no	—
293	C₃	C₂×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
294	C₂	—	6	4	no	—
295	C₂	—	7	4	no	—
296	C₂	—	42	4	no	—
297	C₂	D₁₂×AGL(1,𝔽₇)	1	2	yes	direct product factor
298	C₂	C₂²×D₃×AGL(1,𝔽₇)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃×AGL(1,𝔽₇)
commutator, cosocle	C₂×C₃×C₇	C₂⁴×C₃
Frattini	C₂	C₂²×D₃×AGL(1,𝔽₇)
Fitting	C₂×C₃×C₄×C₇	C₂²×C₃
socle	C₂²×C₃×C₇	C₂³×C₃
hypercenter	C₂×C₄	D₃×AGL(1,𝔽₇)
hypocenter	C₃×C₇	C₂²×C₃×D₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₃×AGL(1,𝔽₇)	C₂	semidirect
2. C₂×C₄⋊(C₃⋊AGL(1,𝔽₇))	C₂	semidirect
3. C₂×ΓL(1,𝔽₈)×D₁₂	C₂	semidirect
4. C₂×C₃×C₄×AGL(1,𝔽₇)	C₂	semidirect
5. C₂×#4247⋊C₃	C₂	semidirect
6. D₁₂×AGL(1,𝔽₇)	C₂	direct (N × H)
7. C₂×D₇×D₁₂	C₃	semidirect
9. C₂²×C₃⋊AGL(1,𝔽₇)	C₂²	semidirect
10. C₂²×D₃×ΓL(1,𝔽₈)	C₂²	semidirect
13. C₂×D₃×AGL(1,𝔽₇)	C₂²	semidirect
14. C₂×C₃×C₄×ΓL(1,𝔽₈)	C₂²	semidirect
15. C₄⋊(C₃⋊AGL(1,𝔽₇))	C₂²	semidirect
16. ΓL(1,𝔽₈)×D₁₂	C₂²	semidirect
17. C₂×C₃×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
18. C₃×C₄×AGL(1,𝔽₇)	C₂²	semidirect
19. #4247⋊C₃	C₂²	semidirect
20. C₂²×D₃×D₇	C₂×C₃	semidirect
22. C₂×D₈₄	C₂×C₃	semidirect
23. C₂×C₇×D₁₂	C₂×C₃	semidirect
24. C₂×C₃×C₄×D₇	C₂×C₃	semidirect
26. C₂×#4247	C₂×C₃	semidirect
27. D₇×D₁₂	C₂×C₃	semidirect
32. C₂×C₄×AGL(1,𝔽₇)	D₃	semidirect
36. C₂×C₃⋊AGL(1,𝔽₇)	C₂³	semidirect
38. C₂×D₃×ΓL(1,𝔽₈)	C₂³	semidirect
39. C₂×C₃×AGL(1,𝔽₇)	D₄	semidirect
42. C₃×C₄×ΓL(1,𝔽₈)	C₂³	semidirect
43. C₃×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
45. C₂²×D₂₁	C₂²×C₃	semidirect
46. C₂²×D₃×C₇	C₂²×C₃	semidirect
50. C₂×D₃×D₇	C₂²×C₃	semidirect
56. C₂×C₃×C₄×C₇	C₂²×C₃	semidirect
57. D₈₄	C₂²×C₃	semidirect
58. C₇×D₁₂	C₂²×C₃	semidirect
59. C₂×C₃×Dic₇	C₂²×C₃	semidirect
60. C₃×C₄×D₇	C₂²×C₃	semidirect
63. C₂×C₄×ΓL(1,𝔽₈)	C₂×D₃	semidirect
64. #4247	C₂²×C₃	semidirect
67. C₂×ΓL(1,𝔽₈)⋊C₄	C₂×D₃	semidirect
70. C₄×AGL(1,𝔽₇)	C₂×D₃	semidirect
77. C₂×C₃×ΓL(1,𝔽₈)	C₂×D₄	semidirect
81. C₃×AGL(1,𝔽₇)	C₂×D₄	semidirect
87. C₂×C₄×D₇	C₃×D₃	semidirect
92. C₂×D₂₁	C₂³×C₃	semidirect
94. C₂×D₃×C₇	C₂³×C₃	semidirect
95. C₂×C₃×D₇	C₃×D₄	semidirect
107. C₂×AGL(1,𝔽₇)	D₁₂	direct (N × H)
109. C₃×C₄×C₇	C₂³×C₃	semidirect
110. C₃×Dic₇	C₂³×C₃	semidirect
112. C₄×ΓL(1,𝔽₈)	C₂²×D₃	semidirect
114. ΓL(1,𝔽₈)⋊C₄	C₂²×D₃	semidirect
126. C₃×ΓL(1,𝔽₈)	C₂²×D₄	semidirect
133. C₂×C₄×C₇	C₂×C₃×D₃	semidirect
135. C₂×Dic₇	C₂×C₃×D₃	semidirect
137. C₄×D₇	C₂×C₃×D₃	semidirect
150. C₂×D₁₂	AGL(1,𝔽₇)	direct (N × H)
151. C₂×C₃×C₇	C₂×C₃×D₄	semidirect
154. C₃×D₇	C₂×C₃×D₄	semidirect
159. C₂×ΓL(1,𝔽₈)	C₂×D₁₂	semidirect
163. AGL(1,𝔽₇)	C₂×D₁₂	direct (N × H)
181. C₂×D₇	C₃×D₁₂	semidirect
183. C₄×C₇	C₂²×C₃×D₃	semidirect
184. Dic₇	C₂²×C₃×D₃	semidirect
195. C₂²×D₃	C₂×AGL(1,𝔽₇)	semidirect
207. C₂×C₃×C₄	C₂×AGL(1,𝔽₇)	semidirect
210. D₁₂	C₂×AGL(1,𝔽₇)	direct (N × H)
211. C₃×C₇	C₂²×C₃×D₄	semidirect
213. ΓL(1,𝔽₈)	C₂²×D₁₂	semidirect
226. C₂×C₇	C₂×C₃×D₁₂	semidirect
229. D₇	C₂×C₃×D₁₂	semidirect
248. C₂×D₃	C₂²×AGL(1,𝔽₇)	semidirect
254. C₃×C₄	C₂²×AGL(1,𝔽₇)	semidirect
266. C₂×C₄	D₃×AGL(1,𝔽₇)	semidirect
267. C₇	C₂²×C₃×D₁₂	semidirect
277. C₂×C₃	D₄×AGL(1,𝔽₇)	semidirect
290. C₄	C₂×D₃×AGL(1,𝔽₇)	semidirect
293. C₃	C₂×D₄×AGL(1,𝔽₇)	semidirect
297. C₂	D₁₂×AGL(1,𝔽₇)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₃×AGL(1,𝔽₇)	2
C₂×C₄⋊(C₃⋊AGL(1,𝔽₇))	2
C₂×ΓL(1,𝔽₈)×D₁₂	2
C₂×C₃×C₄×AGL(1,𝔽₇)	2
C₂×#4247⋊C₃	2
D₁₂×AGL(1,𝔽₇)	2
C₂×D₇×D₁₂	3
C₂×D₄×AGL(1,𝔽₇)	3
C₂²×C₃×D₁₂	7

Subgroups — C2×D12×AGL(1,𝔽7) #72244121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₂×AGL(1,𝔽₇) #72244121