Subgroups — C₂×C₃×#11924174 #72246483

Order 7056.

936 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#10596873	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#10596873	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#87639	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#11924174	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₃×#64424	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924174	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×#11924174	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×#11924174	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×#3861	C₂²	1	1	yes	characteristic
10	C₂×C₃×#64424	C₄	1	4	yes	complemented
11	C₂×C₃×#64424	C₂²	1	2	yes	—
12	C₃×#10596873	C₂²	1	2	yes	complemented
13	C₃×#10596873	C₂²	1	2	yes	complemented
14	C₂²×C₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
15	C₂²×#64424	C₂×C₃	1	1	yes	characteristic
16	C₂²×#64424	C₂×C₃	1	1	yes	characteristic
17	C₂²×#64424	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃×C₇×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂×C₃×C₇×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
20	C₃×#87639	C₂×C₃	1	4	yes	complemented
21	C₂×#10596873	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×#10596873	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂×#10596873	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×#10596873	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#10596873	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#10596873	C₂×C₃	1	1	yes	characteristic, complemented
27	#11924174	C₂×C₃	1	4	yes	direct product factor
28	#11924174	C₂×C₃	1	4	yes	direct product factor
29	#11924174	C₂×C₃	1	4	yes	direct product factor
30	C₂×C₃×C₄×AGL(1,𝔽₇)	—	7	1	no	maximal
31	C₂×C₃×C₄×AGL(1,𝔽₇)	—	7	1	no	maximal
32	C₂×C₃×#3861	C₂×C₄	1	2	yes	complemented
33	C₂×C₃×#3861	C₂³	1	1	yes	characteristic
34	C₃×#64424	C₂×C₄	1	4	yes	complemented
35	C₂×#87639	C₃²	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₃×C₇²	C₂²×C₃	1	1	yes	characteristic
37	C₂×C₃×C₇⋊D₇	C₃×C₄	1	4	yes	complemented
38	C₂×C₃×C₇⋊D₇	C₂²×C₃	1	2	yes	—
39	C₂²×#3861	C₂²×C₃	1	1	yes	characteristic
40	C₂²×#3861	C₂²×C₃	1	1	yes	characteristic
41	C₂²×#3861	C₂²×C₃	1	1	yes	characteristic
42	C₂×#64424	C₃×C₄	1	4	yes	complemented
43	C₂×#64424	C₃×C₄	1	4	yes	complemented
44	C₂×#64424	C₃×C₄	1	4	yes	complemented
45	C₂×#64424	C₂²×C₃	1	2	yes	—
46	C₂×#64424	C₂²×C₃	1	2	yes	—
47	C₂×#64424	C₂²×C₃	1	2	yes	—
48	C₃×C₇×Dic₇	C₂²×C₃	1	2	yes	complemented
49	C₃×C₇×Dic₇	C₂²×C₃	1	2	yes	complemented
50	#10596873	C₂²×C₃	1	2	yes	complemented
51	#10596873	C₂²×C₃	1	2	yes	complemented
52	#10596873	C₂²×C₃	1	2	yes	complemented
53	#10596873	C₂²×C₃	1	2	yes	complemented
54	#10596873	C₂²×C₃	1	2	yes	complemented
55	#10596873	C₂²×C₃	1	2	yes	complemented
56	C₂²×C₃×AGL(1,𝔽₇)	—	7	1	no	—
57	C₂²×C₃×AGL(1,𝔽₇)	—	7	1	no	—
58	C₂²×C₃×AGL(1,𝔽₇)	—	14	1	no	—
59	C₂²×C₃×AGL(1,𝔽₇)	—	14	2	no	—
60	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
61	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
62	C₂×C₃×ΓL(1,𝔽₈)⋊C₄	—	14	1	no	—
63	C₂×C₃×ΓL(1,𝔽₈)⋊C₄	—	14	1	no	—
64	C₃×C₄×AGL(1,𝔽₇)	—	7	4	no	—
65	C₃×C₄×AGL(1,𝔽₇)	—	7	4	no	—
66	C₃×#3861	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
67	C₂²×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic
68	C₂×C₇×Dic₇	C₂×C₃²	1	1	yes	characteristic, complemented
69	C₂×C₇×Dic₇	C₂×C₃²	1	1	yes	characteristic, complemented
70	#87639	C₂×C₃²	1	4	yes	complemented
71	C₂×C₃×C₄×D₇	—	7	1	no	—
72	C₂×C₃×C₄×D₇	—	7	1	no	—
73	C₂×C₄×AGL(1,𝔽₇)	—	7	1	no	—
74	C₂×C₄×AGL(1,𝔽₇)	—	7	1	no	—
75	C₂×C₄×AGL(1,𝔽₇)	—	7	1	no	—
76	C₂×C₄×AGL(1,𝔽₇)	—	7	1	no	—
77	C₂×C₄×AGL(1,𝔽₇)	—	7	1	no	—
78	C₂×C₄×AGL(1,𝔽₇)	—	7	1	no	—
79	C₂×C₃×C₇²	C₂×C₃×C₄	1	2	yes	complemented
80	C₂×C₃×C₇²	C₂³×C₃	1	1	yes	characteristic
81	C₃×C₇⋊D₇	C₂×C₃×C₄	1	4	yes	complemented
82	C₂×#3861	C₂×C₃×C₄	1	2	yes	complemented
83	C₂×#3861	C₂×C₃×C₄	1	2	yes	complemented
84	C₂×#3861	C₂×C₃×C₄	1	2	yes	complemented
85	C₂×#3861	C₂³×C₃	1	1	yes	characteristic
86	C₂×#3861	C₂³×C₃	1	1	yes	characteristic
87	C₂×#3861	C₂³×C₃	1	1	yes	characteristic
88	#64424	C₂×C₃×C₄	1	4	yes	complemented
89	#64424	C₂×C₃×C₄	1	4	yes	complemented
90	#64424	C₂×C₃×C₄	1	4	yes	complemented
91	C₂²×C₃×ΓL(1,𝔽₈)	—	14	1	no	—
92	C₂²×C₃×ΓL(1,𝔽₈)	—	14	1	no	—
93	C₂²×C₃×ΓL(1,𝔽₈)	—	28	1	no	—
94	C₂²×C₃×ΓL(1,𝔽₈)	—	28	2	no	—
95	C₂×C₃×AGL(1,𝔽₇)	—	7	4	no	—
96	C₂×C₃×AGL(1,𝔽₇)	—	7	4	no	—
97	C₂×C₃×AGL(1,𝔽₇)	—	7	2	no	—
98	C₂×C₃×AGL(1,𝔽₇)	—	7	2	no	—
99	C₂×C₃×AGL(1,𝔽₇)	—	14	4	no	—
100	C₂×C₃×AGL(1,𝔽₇)	—	14	8	no	—
101	C₂×C₃×AGL(1,𝔽₇)	—	14	2	no	—
102	C₂×C₃×AGL(1,𝔽₇)	—	14	4	no	—
103	C₃×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
104	C₃×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
105	C₃×ΓL(1,𝔽₈)⋊C₄	—	14	2	no	—
106	C₃×ΓL(1,𝔽₈)⋊C₄	—	14	2	no	—
107	C₂²×C₇²	C₂²×C₃²	1	1	yes	characteristic
108	C₂×C₇⋊D₇	C₃²×C₄	1	4	yes	complemented
109	C₂×C₇⋊D₇	C₂²×C₃²	1	2	yes	—
110	C₇×Dic₇	C₂²×C₃²	1	2	yes	complemented
111	C₇×Dic₇	C₂²×C₃²	1	2	yes	complemented
112	C₂²×C₃×D₇	—	7	1	no	—
113	C₂²×C₃×D₇	—	7	1	no	—
114	C₂²×C₃×D₇	—	14	1	no	—
115	C₂²×C₃×D₇	—	14	2	no	—
116	C₂²×AGL(1,𝔽₇)	—	7	1	no	—
117	C₂²×AGL(1,𝔽₇)	—	7	1	no	—
118	C₂²×AGL(1,𝔽₇)	—	7	1	no	—
119	C₂²×AGL(1,𝔽₇)	—	7	1	no	—
120	C₂²×AGL(1,𝔽₇)	—	7	1	no	—
121	C₂²×AGL(1,𝔽₇)	—	7	1	no	—
122	C₂²×AGL(1,𝔽₇)	—	14	1	no	—
123	C₂²×AGL(1,𝔽₇)	—	14	1	no	—
124	C₂²×AGL(1,𝔽₇)	—	14	1	no	—
125	C₂²×AGL(1,𝔽₇)	—	14	2	no	—
126	C₂²×AGL(1,𝔽₇)	—	14	2	no	—
127	C₂²×AGL(1,𝔽₇)	—	14	2	no	—
128	C₂×C₃×C₄×C₇	—	7	1	no	—
129	C₂×C₃×C₄×C₇	—	7	1	no	—
130	C₂×C₃×Dic₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
131	C₂×C₃×Dic₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
132	C₃×C₄×D₇	—	7	4	no	—
133	C₃×C₄×D₇	—	7	4	no	—
134	C₂×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
135	C₂×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
136	C₂×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
137	C₂×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
138	C₂×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
139	C₂×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
140	C₂×ΓL(1,𝔽₈)⋊C₄	—	7	1	no	—
141	C₂×ΓL(1,𝔽₈)⋊C₄	—	14	1	no	—
142	C₂×ΓL(1,𝔽₈)⋊C₄	—	14	1	no	—
143	C₂×ΓL(1,𝔽₈)⋊C₄	—	14	1	no	—
144	C₂×ΓL(1,𝔽₈)⋊C₄	—	14	1	no	—
145	C₂×ΓL(1,𝔽₈)⋊C₄	—	14	1	no	—
146	C₄×AGL(1,𝔽₇)	—	7	4	no	—
147	C₄×AGL(1,𝔽₇)	—	7	4	no	—
148	C₄×AGL(1,𝔽₇)	—	7	4	no	—
149	C₄×AGL(1,𝔽₇)	—	7	4	no	—
150	C₄×AGL(1,𝔽₇)	—	7	4	no	—
151	C₄×AGL(1,𝔽₇)	—	7	4	no	—
152	C₃×C₇²	C₂²×C₃×C₄	1	1	yes	characteristic, complemented
153	#3861	C₂²×C₃×C₄	1	1	yes	characteristic, complemented
154	#3861	C₂²×C₃×C₄	1	1	yes	characteristic, complemented
155	#3861	C₂²×C₃×C₄	1	1	yes	characteristic, complemented
156	C₂²×C₃²×C₄	—	49	1	no	Hall
157	C₂×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
158	C₂×C₃×ΓL(1,𝔽₈)	—	14	1	no	—
159	C₂×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
160	C₂×C₃×ΓL(1,𝔽₈)	—	14	1	no	—
161	C₂×C₃×ΓL(1,𝔽₈)	—	28	2	no	—
162	C₂×C₃×ΓL(1,𝔽₈)	—	28	1	no	—
163	C₂×C₃×ΓL(1,𝔽₈)	—	28	4	no	—
164	C₂×C₃×ΓL(1,𝔽₈)	—	28	2	no	—
165	C₃×AGL(1,𝔽₇)	—	7	4	no	—
166	C₃×AGL(1,𝔽₇)	—	7	4	no	—
167	C₃×AGL(1,𝔽₇)	—	14	4	no	—
168	C₃×AGL(1,𝔽₇)	—	14	8	no	—
169	C₂×C₄×D₇	—	7	1	no	—
170	C₂×C₄×D₇	—	7	1	no	—
171	C₂×C₇²	C₂×C₃²×C₄	1	2	yes	complemented
172	C₂×C₇²	C₂³×C₃²	1	1	yes	characteristic
173	C₇⋊D₇	C₂×C₃²×C₄	1	4	yes	complemented
174	C₂²×C₃×C₇	—	2	1	no	—
175	C₂²×C₃×C₇	—	2	2	no	—
176	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
177	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
178	C₂×C₃×D₇	—	7	4	no	—
179	C₂×C₃×D₇	—	7	4	no	—
180	C₂×C₃×D₇	—	7	2	no	—
181	C₂×C₃×D₇	—	7	2	no	—
182	C₂×C₃×D₇	—	14	4	no	—
183	C₂×C₃×D₇	—	14	8	no	—
184	C₂×C₃×D₇	—	14	2	no	—
185	C₂×C₃×D₇	—	14	4	no	—
186	C₂²×ΓL(1,𝔽₈)	—	7	1	no	—
187	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
188	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
189	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
190	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
191	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
192	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
193	C₂²×ΓL(1,𝔽₈)	—	28	1	no	—
194	C₂²×ΓL(1,𝔽₈)	—	28	2	no	—
195	C₂²×ΓL(1,𝔽₈)	—	28	1	no	—
196	C₂²×ΓL(1,𝔽₈)	—	28	2	no	—
197	C₂²×ΓL(1,𝔽₈)	—	28	2	no	—
198	C₂×AGL(1,𝔽₇)	—	7	4	no	—
199	C₂×AGL(1,𝔽₇)	—	7	2	no	—
200	C₂×AGL(1,𝔽₇)	—	7	4	no	—
201	C₂×AGL(1,𝔽₇)	—	7	4	no	—
202	C₂×AGL(1,𝔽₇)	—	7	4	no	—
203	C₂×AGL(1,𝔽₇)	—	7	4	no	—
204	C₂×AGL(1,𝔽₇)	—	7	4	no	—
205	C₂×AGL(1,𝔽₇)	—	7	2	no	—
206	C₂×AGL(1,𝔽₇)	—	7	2	no	—
207	C₂×AGL(1,𝔽₇)	—	7	2	no	—
208	C₂×AGL(1,𝔽₇)	—	7	2	no	—
209	C₂×AGL(1,𝔽₇)	—	7	2	no	—
210	C₂×AGL(1,𝔽₇)	—	14	4	no	—
211	C₂×AGL(1,𝔽₇)	—	14	2	no	—
212	C₂×AGL(1,𝔽₇)	—	14	4	no	—
213	C₂×AGL(1,𝔽₇)	—	14	8	no	—
214	C₂×AGL(1,𝔽₇)	—	14	8	no	—
215	C₂×AGL(1,𝔽₇)	—	14	4	no	—
216	C₂×AGL(1,𝔽₇)	—	14	8	no	—
217	C₂×AGL(1,𝔽₇)	—	14	2	no	—
218	C₂×AGL(1,𝔽₇)	—	14	4	no	—
219	C₂×AGL(1,𝔽₇)	—	14	2	no	—
220	C₂×AGL(1,𝔽₇)	—	14	4	no	—
221	C₂×AGL(1,𝔽₇)	—	14	4	no	—
222	C₃×C₄×C₇	—	7	2	no	—
223	C₃×C₄×C₇	—	7	2	no	—
224	C₃×Dic₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
225	C₃×Dic₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
226	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
227	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
228	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
229	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
230	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
231	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
232	ΓL(1,𝔽₈)⋊C₄	—	7	2	no	—
233	ΓL(1,𝔽₈)⋊C₄	—	14	2	no	—
234	ΓL(1,𝔽₈)⋊C₄	—	14	2	no	—
235	ΓL(1,𝔽₈)⋊C₄	—	14	2	no	—
236	ΓL(1,𝔽₈)⋊C₄	—	14	2	no	—
237	ΓL(1,𝔽₈)⋊C₄	—	14	2	no	—
238	C₂³×C₃²	—	49	1	no	—
239	C₂×C₃²×C₄	—	49	4	no	—
240	C₂×C₃²×C₄	—	98	1	no	—
241	C₂×C₃²×C₄	—	98	1	no	—
242	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
243	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
244	C₃×ΓL(1,𝔽₈)	—	28	1	no	—
245	C₃×ΓL(1,𝔽₈)	—	28	2	no	—
246	C₂²×D₇	—	7	1	no	—
247	C₂²×D₇	—	7	1	no	—
248	C₂²×D₇	—	14	1	no	—
249	C₂²×D₇	—	14	2	no	—
250	C₂×C₄×C₇	—	7	1	no	—
251	C₂×C₄×C₇	—	7	1	no	—
252	C₂×Dic₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
253	C₂×Dic₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
254	C₄×D₇	—	7	4	no	—
255	C₄×D₇	—	7	4	no	—
256	C₇²	C₂²×C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
257	C₂²×C₃×C₄	—	49	1	no	—
258	C₂²×C₃×C₄	—	49	1	no	—
259	C₂²×C₃×C₄	—	49	1	no	—
260	C₂²×C₃×C₄	—	49	1	no	—
261	C₂×C₃×C₇	—	2	1	no	—
262	C₂×C₃×C₇	—	2	2	no	—
263	C₂×C₃×C₇	—	2	2	no	—
264	C₂×C₃×C₇	—	2	4	no	—
265	C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	1	2	yes	complemented
266	C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	1	2	yes	complemented
267	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
268	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
269	C₃×D₇	—	7	4	no	—
270	C₃×D₇	—	7	4	no	—
271	C₃×D₇	—	14	4	no	—
272	C₃×D₇	—	14	8	no	—
273	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
274	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
275	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
276	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
277	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
278	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
279	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
280	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
281	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
282	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
283	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
284	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
285	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
286	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
287	C₂×ΓL(1,𝔽₈)	—	28	2	no	—
288	C₂×ΓL(1,𝔽₈)	—	28	4	no	—
289	C₂×ΓL(1,𝔽₈)	—	28	4	no	—
290	C₂×ΓL(1,𝔽₈)	—	28	2	no	—
291	C₂×ΓL(1,𝔽₈)	—	28	4	no	—
292	C₂×ΓL(1,𝔽₈)	—	28	1	no	—
293	C₂×ΓL(1,𝔽₈)	—	28	2	no	—
294	C₂×ΓL(1,𝔽₈)	—	28	1	no	—
295	C₂×ΓL(1,𝔽₈)	—	28	2	no	—
296	C₂×ΓL(1,𝔽₈)	—	28	2	no	—
297	AGL(1,𝔽₇)	—	7	4	no	—
298	AGL(1,𝔽₇)	—	7	4	no	—
299	AGL(1,𝔽₇)	—	7	4	no	—
300	AGL(1,𝔽₇)	—	7	4	no	—
301	AGL(1,𝔽₇)	—	7	4	no	—
302	AGL(1,𝔽₇)	—	7	4	no	—
303	AGL(1,𝔽₇)	—	14	4	no	—
304	AGL(1,𝔽₇)	—	14	4	no	—
305	AGL(1,𝔽₇)	—	14	8	no	—
306	AGL(1,𝔽₇)	—	14	8	no	—
307	AGL(1,𝔽₇)	—	14	4	no	—
308	AGL(1,𝔽₇)	—	14	8	no	—
309	C₂²×C₃²	—	49	2	no	—
310	C₂²×C₃²	—	49	4	no	—
311	C₂²×C₃²	—	196	1	no	—
312	C₃²×C₄	—	98	2	no	—
313	C₃²×C₄	—	98	2	no	—
314	C₂²×C₇	—	2	1	no	—
315	C₂²×C₇	—	2	2	no	—
316	C₂²×C₇	C₂×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
317	C₂²×C₇	C₂×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
318	C₂×D₇	—	7	2	no	—
319	C₂×D₇	—	7	2	no	—
320	C₂×D₇	—	7	4	no	—
321	C₂×D₇	—	7	4	no	—
322	C₂×D₇	—	14	4	no	—
323	C₂×D₇	—	14	8	no	—
324	C₂×D₇	—	14	2	no	—
325	C₂×D₇	—	14	4	no	—
326	C₄×C₇	—	7	2	no	—
327	C₄×C₇	—	7	2	no	—
328	Dic₇	C₂×C₃×AGL(1,𝔽₇)	1	2	yes	complemented
329	Dic₇	C₂×C₃×AGL(1,𝔽₇)	1	2	yes	complemented
330	C₂³×C₃	—	49	1	no	—
331	C₂³×C₃	—	49	1	no	—
332	C₂³×C₃	—	49	1	no	—
333	C₂³×C₃	—	49	1	no	—
334	C₂×C₃×C₄	—	7	1	no	—
335	C₂×C₃×C₄	—	7	1	no	—
336	C₂×C₃×C₄	—	49	1	no	—
337	C₂×C₃×C₄	—	49	4	no	—
338	C₂×C₃×C₄	—	49	4	no	—
339	C₂×C₃×C₄	—	49	4	no	—
340	C₂×C₃×C₄	—	49	4	no	—
341	C₂×C₃×C₄	—	98	1	no	—
342	C₂×C₃×C₄	—	98	1	no	—
343	C₂×C₃×C₄	—	98	1	no	—
344	C₂×C₃×C₄	—	98	1	no	—
345	C₂×C₃×C₄	—	98	1	no	—
346	C₃×C₇	—	2	1	no	—
347	C₃×C₇	—	2	2	no	—
348	C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
349	C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
350	ΓL(1,𝔽₈)	—	7	1	no	—
351	ΓL(1,𝔽₈)	—	14	1	no	—
352	ΓL(1,𝔽₈)	—	14	1	no	—
353	ΓL(1,𝔽₈)	—	14	1	no	—
354	ΓL(1,𝔽₈)	—	14	1	no	—
355	ΓL(1,𝔽₈)	—	14	1	no	—
356	ΓL(1,𝔽₈)	—	14	1	no	—
357	ΓL(1,𝔽₈)	—	28	1	no	—
358	ΓL(1,𝔽₈)	—	28	2	no	—
359	ΓL(1,𝔽₈)	—	28	2	no	—
360	ΓL(1,𝔽₈)	—	28	1	no	—
361	ΓL(1,𝔽₈)	—	28	2	no	—
362	C₂×C₃²	—	49	4	no	—
363	C₂×C₃²	—	196	1	no	—
364	C₂×C₃²	—	196	2	no	—
365	C₂²×C₄	—	49	1	no	Sylow
366	C₂×C₇	—	2	2	no	—
367	C₂×C₇	—	2	4	no	—
368	C₂×C₇	—	2	1	no	—
369	C₂×C₇	—	2	2	no	—
370	C₂×C₇	C₃×C₄×AGL(1,𝔽₇)	1	2	yes	complemented
371	C₂×C₇	C₃×C₄×AGL(1,𝔽₇)	1	2	yes	complemented
372	C₂×C₇	C₂²×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
373	C₂×C₇	C₂²×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
374	D₇	—	7	4	no	—
375	D₇	—	7	4	no	—
376	D₇	—	14	4	no	—
377	D₇	—	14	8	no	—
378	C₂²×C₃	—	49	2	no	—
379	C₂²×C₃	—	49	2	no	—
380	C₂²×C₃	—	49	2	no	—
381	C₂²×C₃	—	49	4	no	—
382	C₂²×C₃	—	49	4	no	—
383	C₂²×C₃	—	49	4	no	—
384	C₂²×C₃	—	49	2	no	—
385	C₂²×C₃	—	49	4	no	—
386	C₂²×C₃	—	196	1	no	—
387	C₂²×C₃	—	196	1	no	—
388	C₂²×C₃	—	196	1	no	—
389	C₂²×C₃	#64423⋊C₂	1	1	yes	characteristic
390	C₃×C₄	—	7	2	no	—
391	C₃×C₄	—	7	2	no	—
392	C₃×C₄	—	49	2	no	—
393	C₃×C₄	—	98	2	no	—
394	C₃×C₄	—	98	2	no	—
395	C₃×C₄	—	98	2	no	—
396	C₃×C₄	—	98	2	no	—
397	C₃×C₄	—	98	2	no	—
398	C₃²	—	196	1	no	Sylow
399	C₂³	—	49	1	no	—
400	C₂×C₄	—	7	1	no	—
401	C₂×C₄	—	7	1	no	—
402	C₂×C₄	—	49	4	no	—
403	C₇	—	2	1	no	—
404	C₇	—	2	2	no	—
405	C₇	C₂×C₃×C₄×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
406	C₇	C₂×C₃×C₄×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
407	C₂×C₃	—	49	4	no	—
408	C₂×C₃	—	49	4	no	—
409	C₂×C₃	—	49	4	no	—
410	C₂×C₃	—	49	4	no	—
411	C₂×C₃	—	196	2	no	—
412	C₂×C₃	—	196	2	no	—
413	C₂×C₃	—	196	2	no	—
414	C₂×C₃	—	196	1	no	—
415	C₂×C₃	—	196	1	no	—
416	C₂×C₃	—	196	1	no	—
417	C₂×C₃	#11924174	1	2	yes	direct product factor
418	C₂×C₃	C₂×#64423⋊C₂	1	1	yes	characteristic
419	C₂²	—	49	4	no	—
420	C₂²	—	49	2	no	—
421	C₂²	C₃×#64423⋊C₂	1	1	yes	characteristic
422	C₄	—	7	2	no	—
423	C₄	—	7	2	no	—
424	C₃	—	196	1	no	—
425	C₃	—	196	1	no	—
426	C₃	—	196	1	no	—
427	C₃	C₂×#11924174	1	1	yes	characteristic, direct product factor
428	C₂	—	49	4	no	—
429	C₂	C₃×#11924174	1	2	yes	direct product factor
430	C₂	C₂×C₃×#64423⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₃	#64423⋊C₂
commutator, hypocenter	C₇²	C₂²×C₃²×C₄
Frattini	C₂	C₂×C₃×#64423⋊C₂
Fitting, socle	C₂²×C₃×C₇²	C₂²×C₃
prime radical	C₂²×C₃×#64424	C₂
cosocle	C₂×C₇²	C₂³×C₃²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#10596873	C₂	semidirect
2. C₂×C₃×#10596873	C₂	semidirect
3. C₂×C₃×#87639	C₃	semidirect
4. C₃×#11924174	C₂	direct (N × H)
6. C₂×#11924174	C₃	direct (N × H)
7. C₂×#11924174	C₃	direct (N × H)
8. C₂×#11924174	C₃	direct (N × H)
10. C₂×C₃×#64424	C₄	semidirect
12. C₃×#10596873	C₂²	semidirect
13. C₃×#10596873	C₂²	semidirect
18. C₂×C₃×C₇×Dic₇	C₂×C₃	semidirect
19. C₂×C₃×C₇×Dic₇	C₂×C₃	semidirect
20. C₃×#87639	C₂×C₃	semidirect
21. C₂×#10596873	C₂×C₃	semidirect
22. C₂×#10596873	C₂×C₃	semidirect
23. C₂×#10596873	C₂×C₃	semidirect
24. C₂×#10596873	C₂×C₃	semidirect
25. C₂×#10596873	C₂×C₃	semidirect
26. C₂×#10596873	C₂×C₃	semidirect
27. #11924174	C₂×C₃	direct (N × H)
28. #11924174	C₂×C₃	direct (N × H)
29. #11924174	C₂×C₃	direct (N × H)
32. C₂×C₃×#3861	C₂×C₄	semidirect
34. C₃×#64424	C₂×C₄	semidirect
35. C₂×#87639	C₃²	semidirect
37. C₂×C₃×C₇⋊D₇	C₃×C₄	semidirect
42. C₂×#64424	C₃×C₄	semidirect
43. C₂×#64424	C₃×C₄	semidirect
44. C₂×#64424	C₃×C₄	semidirect
48. C₃×C₇×Dic₇	C₂²×C₃	semidirect
49. C₃×C₇×Dic₇	C₂²×C₃	semidirect
50. #10596873	C₂²×C₃	semidirect
51. #10596873	C₂²×C₃	semidirect
52. #10596873	C₂²×C₃	semidirect
53. #10596873	C₂²×C₃	semidirect
54. #10596873	C₂²×C₃	semidirect
55. #10596873	C₂²×C₃	semidirect
66. C₃×#3861	C₂²×C₄	semidirect
68. C₂×C₇×Dic₇	C₂×C₃²	semidirect
69. C₂×C₇×Dic₇	C₂×C₃²	semidirect
70. #87639	C₂×C₃²	semidirect
79. C₂×C₃×C₇²	C₂×C₃×C₄	semidirect
81. C₃×C₇⋊D₇	C₂×C₃×C₄	semidirect
82. C₂×#3861	C₂×C₃×C₄	semidirect
83. C₂×#3861	C₂×C₃×C₄	semidirect
84. C₂×#3861	C₂×C₃×C₄	semidirect
88. #64424	C₂×C₃×C₄	semidirect
89. #64424	C₂×C₃×C₄	semidirect
90. #64424	C₂×C₃×C₄	semidirect
108. C₂×C₇⋊D₇	C₃²×C₄	semidirect
110. C₇×Dic₇	C₂²×C₃²	semidirect
111. C₇×Dic₇	C₂²×C₃²	semidirect
130. C₂×C₃×Dic₇	AGL(1,𝔽₇)	semidirect
131. C₂×C₃×Dic₇	AGL(1,𝔽₇)	semidirect
152. C₃×C₇²	C₂²×C₃×C₄	semidirect
153. #3861	C₂²×C₃×C₄	semidirect
154. #3861	C₂²×C₃×C₄	semidirect
155. #3861	C₂²×C₃×C₄	semidirect
171. C₂×C₇²	C₂×C₃²×C₄	semidirect
173. C₇⋊D₇	C₂×C₃²×C₄	semidirect
224. C₃×Dic₇	C₂×AGL(1,𝔽₇)	semidirect
225. C₃×Dic₇	C₂×AGL(1,𝔽₇)	semidirect
252. C₂×Dic₇	C₃×AGL(1,𝔽₇)	semidirect
253. C₂×Dic₇	C₃×AGL(1,𝔽₇)	semidirect
256. C₇²	C₂²×C₃²×C₄	semidirect
265. C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	semidirect
266. C₂×C₃×C₇	C₄×AGL(1,𝔽₇)	semidirect
328. Dic₇	C₂×C₃×AGL(1,𝔽₇)	semidirect
329. Dic₇	C₂×C₃×AGL(1,𝔽₇)	semidirect
348. C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	semidirect
349. C₃×C₇	C₂×C₄×AGL(1,𝔽₇)	semidirect
370. C₂×C₇	C₃×C₄×AGL(1,𝔽₇)	semidirect
371. C₂×C₇	C₃×C₄×AGL(1,𝔽₇)	semidirect
405. C₇	C₂×C₃×C₄×AGL(1,𝔽₇)	semidirect
406. C₇	C₂×C₃×C₄×AGL(1,𝔽₇)	semidirect
417. C₂×C₃	#11924174	direct (N × H)
427. C₃	C₂×#11924174	direct (N × H)
429. C₂	C₃×#11924174	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×#10596873	2
C₂×C₃×#87639	3
C₃×#11924174	2
C₂²×C₃×#64424	2
C₂×#11924174	3
C₂×C₃×C₄×AGL(1,𝔽₇)	7

Subgroups — C2×C3×#11924174 #72246483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#11924174 #72246483