Subgroups — C₂×C₄×C₃⋊#64424 #72245837

Order 7056.

1160 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊#10596874	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×#3861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₃⋊#64424	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₃⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃⋊#64424	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×#64424	—	3	1	no	maximal
7	C₂²×C₃×#3861	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊#64424	C₄	1	4	yes	direct product factor
9	C₂×C₃⋊#64424	C₂²	1	2	yes	—
10	C₃×C₄×#3861	C₂²	1	2	yes	complemented
11	C₃⋊#10596874	C₂²	1	2	yes	complemented
12	C₂²×C₃⋊(C₇⋊D₇)	C₂×C₃	1	1	yes	characteristic
13	C₂²×#64424	—	3	1	no	—
14	C₂×C₃×C₄×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃⋊(C₇⋊Dic₇)	C₂×C₃	1	1	yes	characteristic, complemented
16	C₄×C₃⋊(C₇⋊D₇)	C₂×C₃	1	4	yes	complemented
17	C₂×C₄×#3861	—	2	1	no	—
18	C₂×C₄×#3861	D₃	1	1	yes	characteristic, complemented
19	C₂×#10596874	—	3	1	no	—
20	C₄×#64424	—	3	4	no	—
21	C₂×C₄×C₃⋊AGL(1,𝔽₇)	—	7	1	no	maximal
22	C₂×C₄×C₃⋊AGL(1,𝔽₇)	—	7	1	no	maximal
23	C₂×C₄×C₃⋊AGL(1,𝔽₇)	—	7	3	no	maximal
24	C₂×C₄×C₃⋊AGL(1,𝔽₇)	—	7	3	no	maximal
25	C₂×C₃×#3861	C₂×C₄	1	2	yes	complemented
26	C₂×C₃×#3861	C₂³	1	1	yes	characteristic
27	C₃⋊#64424	C₂×C₄	1	4	yes	direct product factor
28	C₂×C₄×C₇⋊D₇	—	3	1	no	Hall
29	C₂²×C₃×C₇²	C₂²×C₃	1	1	yes	characteristic
30	C₂×C₃⋊(C₇⋊D₇)	C₃×C₄	1	4	yes	complemented
31	C₂×C₃⋊(C₇⋊D₇)	C₂²×C₃	1	2	yes	—
32	C₂²×#3861	—	2	1	no	—
33	C₂²×#3861	C₂×D₃	1	1	yes	characteristic
34	C₂×#64424	—	3	4	no	—
35	C₂×#64424	—	3	2	no	—
36	C₃×C₄×C₇²	C₂²×C₃	1	2	yes	complemented
37	C₃⋊(C₇⋊Dic₇)	C₂²×C₃	1	2	yes	complemented
38	C₄×#3861	—	2	2	no	—
39	C₄×#3861	C₂×D₃	1	2	yes	complemented
40	#10596874	—	3	2	no	—
41	C₂²×C₃⋊AGL(1,𝔽₇)	—	7	1	no	—
42	C₂²×C₃⋊AGL(1,𝔽₇)	—	7	1	no	—
43	C₂²×C₃⋊AGL(1,𝔽₇)	—	7	3	no	—
44	C₂²×C₃⋊AGL(1,𝔽₇)	—	7	3	no	—
45	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
46	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
47	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	14	3	no	—
48	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	14	3	no	—
49	C₂×C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	1	no	—
50	C₂×C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	1	no	—
51	C₂×C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	3	no	—
52	C₂×C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	3	no	—
53	C₄×C₃⋊AGL(1,𝔽₇)	—	7	4	no	—
54	C₄×C₃⋊AGL(1,𝔽₇)	—	7	4	no	—
55	C₄×C₃⋊AGL(1,𝔽₇)	—	7	12	no	—
56	C₄×C₃⋊AGL(1,𝔽₇)	—	7	12	no	—
57	C₃×#3861	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
58	C₂²×C₇⋊D₇	—	3	1	no	—
59	C₂×C₄×C₇²	C₃×D₃	1	1	yes	characteristic, complemented
60	C₂×C₇⋊Dic₇	—	3	1	no	—
61	C₄×C₇⋊D₇	—	3	4	no	—
62	C₂×C₄×D₂₁	—	7	1	no	—
63	C₂×C₄×D₂₁	—	7	1	no	—
64	C₂×C₄×D₂₁	—	7	3	no	—
65	C₂×C₄×D₂₁	—	7	3	no	—
66	C₂×C₄×AGL(1,𝔽₇)	—	21	1	no	—
67	C₂×C₄×AGL(1,𝔽₇)	—	21	3	no	—
68	C₂×C₄×AGL(1,𝔽₇)	—	21	1	no	—
69	C₂×C₄×AGL(1,𝔽₇)	—	21	3	no	—
70	C₂×C₃×C₇²	C₂×C₃×C₄	1	2	yes	complemented
71	C₂×C₃×C₇²	C₂³×C₃	1	1	yes	characteristic
72	C₃⋊(C₇⋊D₇)	C₂×C₃×C₄	1	4	yes	complemented
73	C₂×#3861	—	2	2	no	—
74	C₂×#3861	—	2	1	no	—
75	C₂×#3861	C₄×D₃	1	2	yes	complemented
76	C₂×#3861	C₂²×D₃	1	1	yes	characteristic
77	#64424	—	3	4	no	—
78	C₂²×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
79	C₂²×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
80	C₂²×C₃×ΓL(1,𝔽₈)	—	14	3	no	—
81	C₂²×C₃×ΓL(1,𝔽₈)	—	14	3	no	—
82	C₂×C₃⋊AGL(1,𝔽₇)	—	7	4	no	—
83	C₂×C₃⋊AGL(1,𝔽₇)	—	7	4	no	—
84	C₂×C₃⋊AGL(1,𝔽₇)	—	7	2	no	—
85	C₂×C₃⋊AGL(1,𝔽₇)	—	7	2	no	—
86	C₂×C₃⋊AGL(1,𝔽₇)	—	7	12	no	—
87	C₂×C₃⋊AGL(1,𝔽₇)	—	7	12	no	—
88	C₂×C₃⋊AGL(1,𝔽₇)	—	7	6	no	—
89	C₂×C₃⋊AGL(1,𝔽₇)	—	7	6	no	—
90	C₃×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
91	C₃×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
92	C₃×C₄×ΓL(1,𝔽₈)	—	14	6	no	—
93	C₃×C₄×ΓL(1,𝔽₈)	—	14	6	no	—
94	C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	2	no	—
95	C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	2	no	—
96	C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	6	no	—
97	C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	6	no	—
98	C₂²×C₇²	C₂×C₃×D₃	1	1	yes	characteristic
99	C₂×C₇⋊D₇	—	3	4	no	—
100	C₂×C₇⋊D₇	—	3	2	no	—
101	C₄×C₇²	C₂×C₃×D₃	1	2	yes	complemented
102	C₇⋊Dic₇	—	3	2	no	—
103	C₂²×D₂₁	—	7	1	no	—
104	C₂²×D₂₁	—	7	1	no	—
105	C₂²×D₂₁	—	7	3	no	—
106	C₂²×D₂₁	—	7	3	no	—
107	C₂²×AGL(1,𝔽₇)	—	21	1	no	—
108	C₂²×AGL(1,𝔽₇)	—	21	3	no	—
109	C₂²×AGL(1,𝔽₇)	—	21	1	no	—
110	C₂²×AGL(1,𝔽₇)	—	21	3	no	—
111	C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
112	C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
113	C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	1	3	yes	complemented
114	C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	1	3	yes	complemented
115	C₂×Dic₂₁	—	7	1	no	—
116	C₂×Dic₂₁	—	7	1	no	—
117	C₂×Dic₂₁	—	7	3	no	—
118	C₂×Dic₂₁	—	7	3	no	—
119	C₄×D₂₁	—	7	4	no	—
120	C₄×D₂₁	—	7	4	no	—
121	C₄×D₂₁	—	7	12	no	—
122	C₄×D₂₁	—	7	12	no	—
123	C₂×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
124	C₂×C₄×ΓL(1,𝔽₈)	—	7	3	no	—
125	C₂×C₄×ΓL(1,𝔽₈)	—	14	1	no	—
126	C₂×C₄×ΓL(1,𝔽₈)	—	14	1	no	—
127	C₂×C₄×ΓL(1,𝔽₈)	—	14	1	no	—
128	C₂×C₄×ΓL(1,𝔽₈)	—	14	3	no	—
129	C₂×C₄×ΓL(1,𝔽₈)	—	14	3	no	—
130	C₂×C₄×ΓL(1,𝔽₈)	—	14	3	no	—
131	C₂×ΓL(1,𝔽₈)⋊C₄	—	21	1	no	—
132	C₂×ΓL(1,𝔽₈)⋊C₄	—	21	3	no	—
133	C₂×ΓL(1,𝔽₈)⋊C₄	—	21	1	no	—
134	C₂×ΓL(1,𝔽₈)⋊C₄	—	21	3	no	—
135	C₄×AGL(1,𝔽₇)	—	21	4	no	—
136	C₄×AGL(1,𝔽₇)	—	21	12	no	—
137	C₄×AGL(1,𝔽₇)	—	21	4	no	—
138	C₄×AGL(1,𝔽₇)	—	21	12	no	—
139	C₃×C₇²	C₂²×C₃×C₄	1	1	yes	characteristic, complemented
140	#3861	—	2	1	no	—
141	#3861	C₂×C₄×D₃	1	1	yes	characteristic, complemented
142	C₂×C₃×C₄×D₃	—	49	1	no	Hall
143	C₂×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
144	C₂×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
145	C₂×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
146	C₂×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
147	C₂×C₃×ΓL(1,𝔽₈)	—	14	6	no	—
148	C₂×C₃×ΓL(1,𝔽₈)	—	14	3	no	—
149	C₂×C₃×ΓL(1,𝔽₈)	—	14	6	no	—
150	C₂×C₃×ΓL(1,𝔽₈)	—	14	3	no	—
151	C₃⋊AGL(1,𝔽₇)	—	7	4	no	—
152	C₃⋊AGL(1,𝔽₇)	—	7	4	no	—
153	C₃⋊AGL(1,𝔽₇)	—	7	12	no	—
154	C₃⋊AGL(1,𝔽₇)	—	7	12	no	—
155	C₂×C₄×D₇	—	21	1	no	—
156	C₂×C₄×D₇	—	21	3	no	—
157	C₂×C₄×D₇	—	21	1	no	—
158	C₂×C₄×D₇	—	21	3	no	—
159	C₂×C₇²	C₃×C₄×D₃	1	2	yes	complemented
160	C₂×C₇²	C₂²×C₃×D₃	1	1	yes	characteristic
161	C₇⋊D₇	—	3	4	no	—
162	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
163	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
164	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	3	yes	—
165	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	3	yes	—
166	C₂×D₂₁	—	7	4	no	—
167	C₂×D₂₁	—	7	4	no	—
168	C₂×D₂₁	—	7	12	no	—
169	C₂×D₂₁	—	7	12	no	—
170	C₂×D₂₁	—	7	2	no	—
171	C₂×D₂₁	—	7	2	no	—
172	C₂×D₂₁	—	7	6	no	—
173	C₂×D₂₁	—	7	6	no	—
174	C₂²×ΓL(1,𝔽₈)	—	7	1	no	—
175	C₂²×ΓL(1,𝔽₈)	—	7	3	no	—
176	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
177	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
178	C₂²×ΓL(1,𝔽₈)	—	14	3	no	—
179	C₂²×ΓL(1,𝔽₈)	—	14	3	no	—
180	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
181	C₂²×ΓL(1,𝔽₈)	—	14	3	no	—
182	C₂×AGL(1,𝔽₇)	—	21	2	no	—
183	C₂×AGL(1,𝔽₇)	—	21	6	no	—
184	C₂×AGL(1,𝔽₇)	—	21	4	no	—
185	C₂×AGL(1,𝔽₇)	—	21	12	no	—
186	C₂×AGL(1,𝔽₇)	—	21	2	no	—
187	C₂×AGL(1,𝔽₇)	—	21	6	no	—
188	C₂×AGL(1,𝔽₇)	—	21	4	no	—
189	C₂×AGL(1,𝔽₇)	—	21	12	no	—
190	C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
191	C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
192	C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	1	6	yes	complemented
193	C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	1	6	yes	complemented
194	Dic₂₁	—	7	2	no	—
195	Dic₂₁	—	7	2	no	—
196	Dic₂₁	—	7	6	no	—
197	Dic₂₁	—	7	6	no	—
198	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
199	C₄×ΓL(1,𝔽₈)	—	7	6	no	—
200	C₄×ΓL(1,𝔽₈)	—	14	2	no	—
201	C₄×ΓL(1,𝔽₈)	—	14	2	no	—
202	C₄×ΓL(1,𝔽₈)	—	14	6	no	—
203	C₄×ΓL(1,𝔽₈)	—	14	6	no	—
204	C₄×ΓL(1,𝔽₈)	—	14	2	no	—
205	C₄×ΓL(1,𝔽₈)	—	14	6	no	—
206	ΓL(1,𝔽₈)⋊C₄	—	21	2	no	—
207	ΓL(1,𝔽₈)⋊C₄	—	21	6	no	—
208	ΓL(1,𝔽₈)⋊C₄	—	21	2	no	—
209	ΓL(1,𝔽₈)⋊C₄	—	21	6	no	—
210	C₂²×C₃×D₃	—	49	1	no	—
211	C₂×C₃²×C₄	—	98	1	no	—
212	C₂×C₃×Dic₃	—	49	1	no	—
213	C₃×C₄×D₃	—	49	4	no	—
214	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
215	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
216	C₃×ΓL(1,𝔽₈)	—	14	3	no	—
217	C₃×ΓL(1,𝔽₈)	—	14	3	no	—
218	C₂²×D₇	—	21	1	no	—
219	C₂²×D₇	—	21	3	no	—
220	C₂²×D₇	—	21	1	no	—
221	C₂²×D₇	—	21	3	no	—
222	C₂×C₄×C₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
223	C₂×C₄×C₇	C₃⋊AGL(1,𝔽₇)	1	3	yes	complemented
224	C₂×C₄×C₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
225	C₂×C₄×C₇	C₃⋊AGL(1,𝔽₇)	1	3	yes	complemented
226	C₂×Dic₇	—	21	1	no	—
227	C₂×Dic₇	—	21	3	no	—
228	C₂×Dic₇	—	21	1	no	—
229	C₂×Dic₇	—	21	3	no	—
230	C₄×D₇	—	21	4	no	—
231	C₄×D₇	—	21	12	no	—
232	C₄×D₇	—	21	4	no	—
233	C₄×D₇	—	21	12	no	—
234	C₇²	C₂×C₃×C₄×D₃	1	1	yes	characteristic, complemented, Sylow
235	C₂²×C₃×C₄	—	147	1	no	—
236	C₂×C₄×D₃	—	49	1	no	—
237	C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	1	2	yes	complemented
238	C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	1	2	yes	complemented
239	C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	1	6	yes	complemented
240	C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	1	6	yes	complemented
241	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
242	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
243	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	3	yes	—
244	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	3	yes	—
245	D₂₁	—	7	4	no	—
246	D₂₁	—	7	4	no	—
247	D₂₁	—	7	12	no	—
248	D₂₁	—	7	12	no	—
249	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
250	C₂×ΓL(1,𝔽₈)	—	7	3	no	—
251	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
252	C₂×ΓL(1,𝔽₈)	—	7	6	no	—
253	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
254	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
255	C₂×ΓL(1,𝔽₈)	—	14	3	no	—
256	C₂×ΓL(1,𝔽₈)	—	14	3	no	—
257	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
258	C₂×ΓL(1,𝔽₈)	—	14	3	no	—
259	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
260	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
261	C₂×ΓL(1,𝔽₈)	—	14	6	no	—
262	C₂×ΓL(1,𝔽₈)	—	14	6	no	—
263	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
264	C₂×ΓL(1,𝔽₈)	—	14	6	no	—
265	AGL(1,𝔽₇)	—	21	4	no	—
266	AGL(1,𝔽₇)	—	21	12	no	—
267	AGL(1,𝔽₇)	—	21	4	no	—
268	AGL(1,𝔽₇)	—	21	12	no	—
269	C₂²×C₃²	—	98	1	no	—
270	C₂×C₃×D₃	—	49	2	no	—
271	C₂×C₃×D₃	—	49	4	no	—
272	C₃²×C₄	—	98	2	no	—
273	C₃×Dic₃	—	49	2	no	—
274	C₂²×C₇	C₂×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic
275	C₂²×C₇	C₂×C₃⋊AGL(1,𝔽₇)	1	3	yes	—
276	C₂²×C₇	C₂×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic
277	C₂²×C₇	C₂×C₃⋊AGL(1,𝔽₇)	1	3	yes	—
278	C₂×D₇	—	21	2	no	—
279	C₂×D₇	—	21	6	no	—
280	C₂×D₇	—	21	2	no	—
281	C₂×D₇	—	21	6	no	—
282	C₂×D₇	—	21	4	no	—
283	C₂×D₇	—	21	12	no	—
284	C₂×D₇	—	21	4	no	—
285	C₂×D₇	—	21	12	no	—
286	C₄×C₇	C₂×C₃⋊AGL(1,𝔽₇)	1	2	yes	complemented
287	C₄×C₇	C₂×C₃⋊AGL(1,𝔽₇)	1	6	yes	complemented
288	C₄×C₇	C₂×C₃⋊AGL(1,𝔽₇)	1	2	yes	complemented
289	C₄×C₇	C₂×C₃⋊AGL(1,𝔽₇)	1	6	yes	complemented
290	Dic₇	—	21	2	no	—
291	Dic₇	—	21	6	no	—
292	Dic₇	—	21	2	no	—
293	Dic₇	—	21	6	no	—
294	C₂³×C₃	—	147	1	no	—
295	C₂²×D₃	—	49	1	no	—
296	C₂×C₃×C₄	—	98	1	no	—
297	C₂×C₃×C₄	—	98	1	no	—
298	C₂×C₃×C₄	—	147	4	no	—
299	C₂×C₃×C₄	—	147	1	no	—
300	C₂×C₃×C₄	#64424	1	1	yes	characteristic, complemented
301	C₂×Dic₃	—	49	1	no	—
302	C₄×D₃	—	49	4	no	—
303	C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
304	C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
305	C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	1	3	yes	complemented
306	C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	1	3	yes	complemented
307	ΓL(1,𝔽₈)	—	7	1	no	—
308	ΓL(1,𝔽₈)	—	7	3	no	—
309	ΓL(1,𝔽₈)	—	14	1	no	—
310	ΓL(1,𝔽₈)	—	14	1	no	—
311	ΓL(1,𝔽₈)	—	14	3	no	—
312	ΓL(1,𝔽₈)	—	14	3	no	—
313	ΓL(1,𝔽₈)	—	14	1	no	—
314	ΓL(1,𝔽₈)	—	14	3	no	—
315	C₂×C₃²	—	98	1	no	—
316	C₂×C₃²	—	98	2	no	—
317	C₃×D₃	—	49	4	no	—
318	C₂²×C₄	—	147	1	no	Sylow
319	C₂×C₇	C₄×C₃⋊AGL(1,𝔽₇)	1	2	yes	complemented
320	C₂×C₇	C₄×C₃⋊AGL(1,𝔽₇)	1	6	yes	complemented
321	C₂×C₇	C₄×C₃⋊AGL(1,𝔽₇)	1	2	yes	complemented
322	C₂×C₇	C₄×C₃⋊AGL(1,𝔽₇)	1	6	yes	complemented
323	C₂×C₇	C₂²×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic
324	C₂×C₇	C₂²×C₃⋊AGL(1,𝔽₇)	1	3	yes	—
325	C₂×C₇	C₂²×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic
326	C₂×C₇	C₂²×C₃⋊AGL(1,𝔽₇)	1	3	yes	—
327	D₇	—	21	4	no	—
328	D₇	—	21	12	no	—
329	D₇	—	21	4	no	—
330	D₇	—	21	12	no	—
331	C₂²×C₃	—	98	1	no	—
332	C₂²×C₃	—	98	1	no	—
333	C₂²×C₃	—	147	2	no	—
334	C₂²×C₃	—	147	4	no	—
335	C₂²×C₃	C₂×#64424	1	1	yes	characteristic
336	C₂×D₃	—	49	2	no	—
337	C₂×D₃	—	49	4	no	—
338	C₃×C₄	—	98	2	no	—
339	C₃×C₄	—	98	2	no	—
340	C₃×C₄	—	147	2	no	—
341	C₃×C₄	C₂×#64424	1	2	yes	complemented
342	Dic₃	—	49	2	no	—
343	C₃²	—	98	1	no	Sylow
344	C₂³	—	147	1	no	—
345	C₂×C₄	—	147	1	no	—
346	C₂×C₄	—	147	4	no	—
347	C₂×C₄	C₃⋊#64424	1	1	yes	characteristic, direct product factor
348	C₇	C₂×C₄×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
349	C₇	C₂×C₄×C₃⋊AGL(1,𝔽₇)	1	3	yes	complemented
350	C₇	C₂×C₄×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
351	C₇	C₂×C₄×C₃⋊AGL(1,𝔽₇)	1	3	yes	complemented
352	C₂×C₃	—	98	2	no	—
353	C₂×C₃	—	98	2	no	—
354	C₂×C₃	—	98	1	no	—
355	C₂×C₃	—	98	1	no	—
356	C₂×C₃	—	147	4	no	—
357	C₂×C₃	C₄×#64424	1	2	yes	complemented
358	C₂×C₃	C₂²×#64424	1	1	yes	characteristic
359	D₃	—	49	4	no	—
360	C₂²	—	147	4	no	—
361	C₂²	—	147	2	no	—
362	C₂²	C₂×C₃⋊#64424	1	1	yes	characteristic
363	C₄	—	147	2	no	—
364	C₄	C₂×C₃⋊#64424	1	2	yes	direct product factor
365	C₃	—	98	1	no	—
366	C₃	—	98	1	no	—
367	C₃	C₂×C₄×#64424	1	1	yes	characteristic, complemented
368	C₂	—	147	4	no	—
369	C₂	C₂²×C₃⋊#64424	1	1	yes	characteristic
370	C₂	C₄×C₃⋊#64424	1	2	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄	C₃⋊#64424
commutator, hypocenter	C₃×C₇²	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃⋊#64424
Fitting	C₂×C₃×C₄×C₇²	C₂×C₃
socle	C₂²×C₃×C₇²	C₂²×C₃
prime radical	C₂²×C₃⋊#64424	C₂
cosocle	C₂×C₃×C₇²	C₂³×C₃
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊#10596874	C₂	semidirect
2. C₂×C₃×C₄×#3861	C₂	semidirect
3. C₄×C₃⋊#64424	C₂	direct (N × H)
4. C₂×C₄×C₃⋊(C₇⋊D₇)	C₃	semidirect
8. C₂×C₃⋊#64424	C₄	direct (N × H)
10. C₃×C₄×#3861	C₂²	semidirect
11. C₃⋊#10596874	C₂²	semidirect
14. C₂×C₃×C₄×C₇²	C₂×C₃	semidirect
15. C₂×C₃⋊(C₇⋊Dic₇)	C₂×C₃	semidirect
16. C₄×C₃⋊(C₇⋊D₇)	C₂×C₃	semidirect
18. C₂×C₄×#3861	D₃	semidirect
25. C₂×C₃×#3861	C₂×C₄	semidirect
27. C₃⋊#64424	C₂×C₄	direct (N × H)
30. C₂×C₃⋊(C₇⋊D₇)	C₃×C₄	semidirect
36. C₃×C₄×C₇²	C₂²×C₃	semidirect
37. C₃⋊(C₇⋊Dic₇)	C₂²×C₃	semidirect
39. C₄×#3861	C₂×D₃	semidirect
57. C₃×#3861	C₂²×C₄	semidirect
59. C₂×C₄×C₇²	C₃×D₃	semidirect
70. C₂×C₃×C₇²	C₂×C₃×C₄	semidirect
72. C₃⋊(C₇⋊D₇)	C₂×C₃×C₄	semidirect
75. C₂×#3861	C₄×D₃	semidirect
101. C₄×C₇²	C₂×C₃×D₃	semidirect
111. C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	semidirect
112. C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	semidirect
113. C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	semidirect
114. C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	semidirect
139. C₃×C₇²	C₂²×C₃×C₄	semidirect
141. #3861	C₂×C₄×D₃	semidirect
159. C₂×C₇²	C₃×C₄×D₃	semidirect
190. C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
191. C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
192. C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
193. C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
222. C₂×C₄×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
223. C₂×C₄×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
224. C₂×C₄×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
225. C₂×C₄×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
234. C₇²	C₂×C₃×C₄×D₃	semidirect
237. C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	semidirect
238. C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	semidirect
239. C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	semidirect
240. C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	semidirect
286. C₄×C₇	C₂×C₃⋊AGL(1,𝔽₇)	semidirect
287. C₄×C₇	C₂×C₃⋊AGL(1,𝔽₇)	semidirect
288. C₄×C₇	C₂×C₃⋊AGL(1,𝔽₇)	semidirect
289. C₄×C₇	C₂×C₃⋊AGL(1,𝔽₇)	semidirect
300. C₂×C₃×C₄	#64424	semidirect
303. C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	semidirect
304. C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	semidirect
305. C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	semidirect
306. C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	semidirect
319. C₂×C₇	C₄×C₃⋊AGL(1,𝔽₇)	semidirect
320. C₂×C₇	C₄×C₃⋊AGL(1,𝔽₇)	semidirect
321. C₂×C₇	C₄×C₃⋊AGL(1,𝔽₇)	semidirect
322. C₂×C₇	C₄×C₃⋊AGL(1,𝔽₇)	semidirect
341. C₃×C₄	C₂×#64424	semidirect
347. C₂×C₄	C₃⋊#64424	direct (N × H)
348. C₇	C₂×C₄×C₃⋊AGL(1,𝔽₇)	semidirect
349. C₇	C₂×C₄×C₃⋊AGL(1,𝔽₇)	semidirect
350. C₇	C₂×C₄×C₃⋊AGL(1,𝔽₇)	semidirect
351. C₇	C₂×C₄×C₃⋊AGL(1,𝔽₇)	semidirect
357. C₂×C₃	C₄×#64424	semidirect
364. C₄	C₂×C₃⋊#64424	direct (N × H)
367. C₃	C₂×C₄×#64424	semidirect
370. C₂	C₄×C₃⋊#64424	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃⋊#10596874	2
C₂×C₃×C₄×#3861	2
C₄×C₃⋊#64424	2
C₂×C₄×C₃⋊(C₇⋊D₇)	3
C₂²×C₃⋊#64424	2
C₂×C₄×#64424	3
C₂×C₄×C₃⋊AGL(1,𝔽₇)	7

Subgroups — C2×C4×C3⋊#64424 #72245837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₃⋊#64424 #72245837