Subgroups — C₂×C₃×C₄⋊#64424 #72245988

Order 7056.

1620 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊#64424	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₃×C₄×#3861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#64424	C₂	1	2	yes	maximal, complemented
5	C₂×C₄⋊#64424	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₄⋊#64424	C₃	1	2	yes	maximal, direct product factor
7	C₂²×C₃×#3861	C₂²	1	1	yes	characteristic
8	C₂×C₃×#64424	—	2	4	no	—
9	C₂×C₃×#64424	C₂²	1	4	yes	complemented
10	C₃×C₄×#3861	C₂²	1	2	yes	complemented
11	C₂²×C₃×C₇⋊D₇	C₂×C₃	1	2	yes	complemented
12	C₂²×#64424	C₂×C₃	1	2	yes	complemented
13	C₂²×#64424	C₂×C₃	1	4	yes	complemented
14	C₂×C₃×C₄×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
15	C₃×C₄⋊(C₇⋊D₇)	C₂×C₃	1	4	yes	complemented
16	C₂×C₄×#3861	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂×C₄×#3861	C₂×C₃	1	2	yes	complemented
18	C₄⋊#64424	C₂×C₃	1	4	yes	direct product factor
19	C₄⋊#64424	C₂×C₃	1	8	yes	direct product factor
20	C₂×C₃×C₄⋊AGL(1,𝔽₇)	—	7	1	no	maximal
21	C₂×C₃×C₄⋊AGL(1,𝔽₇)	—	7	2	no	maximal
22	C₂×C₃×C₄⋊AGL(1,𝔽₇)	—	7	2	no	maximal
23	C₂×C₃×C₄⋊AGL(1,𝔽₇)	—	7	3	no	maximal
24	C₂×C₃×#3861	D₄	1	2	yes	complemented
25	C₂×C₃×#3861	C₂³	1	1	yes	characteristic
26	C₃×#64424	—	2	4	no	—
27	C₂×C₄⋊(C₇⋊D₇)	C₃²	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₃×C₇²	C₂²×C₃	1	1	yes	characteristic
29	C₂×C₃×C₇⋊D₇	—	2	4	no	—
30	C₂×C₃×C₇⋊D₇	C₂²×C₃	1	4	yes	complemented
31	C₂²×#3861	C₂²×C₃	1	1	yes	characteristic
32	C₂²×#3861	C₂²×C₃	1	2	yes	—
33	C₂×#64424	—	2	4	no	—
34	C₂×#64424	—	2	8	no	—
35	C₂×#64424	C₂²×C₃	1	4	yes	complemented
36	C₂×#64424	C₂²×C₃	1	8	yes	complemented
37	C₃×C₄×C₇²	C₂²×C₃	1	2	yes	complemented
38	C₄×#3861	C₂²×C₃	1	2	yes	complemented
39	C₄×#3861	C₂²×C₃	1	4	yes	complemented
40	C₂²×C₃×AGL(1,𝔽₇)	—	7	2	no	—
41	C₂²×C₃×AGL(1,𝔽₇)	—	7	4	no	—
42	C₂²×C₃×AGL(1,𝔽₇)	—	7	4	no	—
43	C₂²×C₃×AGL(1,𝔽₇)	—	7	6	no	—
44	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
45	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
46	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	14	2	no	—
47	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	14	3	no	—
48	C₃×C₄⋊AGL(1,𝔽₇)	—	7	4	no	—
49	C₃×C₄⋊AGL(1,𝔽₇)	—	7	8	no	—
50	C₃×C₄⋊AGL(1,𝔽₇)	—	7	8	no	—
51	C₃×C₄⋊AGL(1,𝔽₇)	—	7	12	no	—
52	C₃×#3861	C₂×D₄	1	1	yes	characteristic, complemented, Hall
53	C₂²×C₇⋊D₇	C₂×C₃²	1	2	yes	complemented
54	C₂×C₄×C₇²	C₂×C₃²	1	1	yes	characteristic, complemented
55	C₄⋊(C₇⋊D₇)	C₂×C₃²	1	4	yes	complemented
56	C₂×C₃×D₂₈	—	7	1	no	—
57	C₂×C₃×D₂₈	—	7	2	no	—
58	C₂×C₃×D₂₈	—	7	2	no	—
59	C₂×C₃×D₂₈	—	7	3	no	—
60	C₂×C₄⋊AGL(1,𝔽₇)	—	7	1	no	—
61	C₂×C₄⋊AGL(1,𝔽₇)	—	7	2	no	—
62	C₂×C₄⋊AGL(1,𝔽₇)	—	7	2	no	—
63	C₂×C₄⋊AGL(1,𝔽₇)	—	7	2	no	—
64	C₂×C₄⋊AGL(1,𝔽₇)	—	7	4	no	—
65	C₂×C₄⋊AGL(1,𝔽₇)	—	7	4	no	—
66	C₂×C₄⋊AGL(1,𝔽₇)	—	7	3	no	—
67	C₂×C₄⋊AGL(1,𝔽₇)	—	7	6	no	—
68	C₂×C₃×C₇²	C₃×D₄	1	2	yes	complemented
69	C₂×C₃×C₇²	C₂³×C₃	1	1	yes	characteristic
70	C₃×C₇⋊D₇	—	2	4	no	—
71	C₂×#3861	C₃×D₄	1	2	yes	complemented
72	C₂×#3861	C₃×D₄	1	4	yes	complemented
73	C₂×#3861	C₂³×C₃	1	1	yes	characteristic
74	C₂×#3861	C₂³×C₃	1	2	yes	—
75	#64424	—	2	4	no	—
76	#64424	—	2	8	no	—
77	C₂²×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
78	C₂²×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
79	C₂²×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
80	C₂²×C₃×ΓL(1,𝔽₈)	—	14	3	no	—
81	C₂×C₃×AGL(1,𝔽₇)	—	7	4	no	—
82	C₂×C₃×AGL(1,𝔽₇)	—	7	8	no	—
83	C₂×C₃×AGL(1,𝔽₇)	—	7	8	no	—
84	C₂×C₃×AGL(1,𝔽₇)	—	7	12	no	—
85	C₂×C₃×AGL(1,𝔽₇)	—	14	4	no	—
86	C₂×C₃×AGL(1,𝔽₇)	—	14	8	no	—
87	C₂×C₃×AGL(1,𝔽₇)	—	14	8	no	—
88	C₂×C₃×AGL(1,𝔽₇)	—	14	12	no	—
89	C₃×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
90	C₃×C₄×ΓL(1,𝔽₈)	—	7	4	no	—
91	C₃×C₄×ΓL(1,𝔽₈)	—	14	4	no	—
92	C₃×C₄×ΓL(1,𝔽₈)	—	14	6	no	—
93	C₂²×C₇²	C₂²×C₃²	1	1	yes	characteristic
94	C₂×C₇⋊D₇	—	2	4	no	—
95	C₂×C₇⋊D₇	C₂²×C₃²	1	4	yes	complemented
96	C₄×C₇²	C₂²×C₃²	1	2	yes	complemented
97	C₂²×C₃×D₇	—	7	2	no	—
98	C₂²×C₃×D₇	—	7	4	no	—
99	C₂²×C₃×D₇	—	7	4	no	—
100	C₂²×C₃×D₇	—	7	6	no	—
101	C₂²×AGL(1,𝔽₇)	—	7	2	no	—
102	C₂²×AGL(1,𝔽₇)	—	7	4	no	—
103	C₂²×AGL(1,𝔽₇)	—	7	4	no	—
104	C₂²×AGL(1,𝔽₇)	—	7	4	no	—
105	C₂²×AGL(1,𝔽₇)	—	7	8	no	—
106	C₂²×AGL(1,𝔽₇)	—	7	8	no	—
107	C₂²×AGL(1,𝔽₇)	—	7	6	no	—
108	C₂²×AGL(1,𝔽₇)	—	7	12	no	—
109	C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
110	C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	1	2	yes	complemented
111	C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	1	2	yes	complemented
112	C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	1	3	yes	complemented
113	C₃×D₂₈	—	7	4	no	—
114	C₃×D₂₈	—	7	8	no	—
115	C₃×D₂₈	—	7	8	no	—
116	C₃×D₂₈	—	7	12	no	—
117	C₂×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
118	C₂×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
119	C₂×C₄×ΓL(1,𝔽₈)	—	14	2	no	—
120	C₂×C₄×ΓL(1,𝔽₈)	—	14	2	no	—
121	C₂×C₄×ΓL(1,𝔽₈)	—	14	4	no	—
122	C₂×C₄×ΓL(1,𝔽₈)	—	14	4	no	—
123	C₂×C₄×ΓL(1,𝔽₈)	—	14	3	no	—
124	C₂×C₄×ΓL(1,𝔽₈)	—	14	6	no	—
125	C₄⋊AGL(1,𝔽₇)	—	7	4	no	—
126	C₄⋊AGL(1,𝔽₇)	—	7	8	no	—
127	C₄⋊AGL(1,𝔽₇)	—	7	8	no	—
128	C₄⋊AGL(1,𝔽₇)	—	7	8	no	—
129	C₄⋊AGL(1,𝔽₇)	—	7	16	no	—
130	C₄⋊AGL(1,𝔽₇)	—	7	16	no	—
131	C₄⋊AGL(1,𝔽₇)	—	7	12	no	—
132	C₄⋊AGL(1,𝔽₇)	—	7	24	no	—
133	C₃×C₇²	C₂×C₃×D₄	1	1	yes	characteristic, complemented
134	#3861	C₂×C₃×D₄	1	1	yes	characteristic, complemented
135	#3861	C₂×C₃×D₄	1	2	yes	complemented
136	C₂×C₃²×D₄	—	49	1	no	Hall
137	C₂×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
138	C₂×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
139	C₂×C₃×ΓL(1,𝔽₈)	—	7	4	no	—
140	C₂×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
141	C₂×C₃×ΓL(1,𝔽₈)	—	14	4	no	—
142	C₂×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
143	C₂×C₃×ΓL(1,𝔽₈)	—	14	6	no	—
144	C₂×C₃×ΓL(1,𝔽₈)	—	14	3	no	—
145	C₃×AGL(1,𝔽₇)	—	14	4	no	—
146	C₃×AGL(1,𝔽₇)	—	14	8	no	—
147	C₃×AGL(1,𝔽₇)	—	14	8	no	—
148	C₃×AGL(1,𝔽₇)	—	14	12	no	—
149	C₂×D₂₈	—	7	1	no	—
150	C₂×D₂₈	—	7	2	no	—
151	C₂×D₂₈	—	7	2	no	—
152	C₂×D₂₈	—	7	3	no	—
153	C₂×C₇²	C₃²×D₄	1	2	yes	complemented
154	C₂×C₇²	C₂³×C₃²	1	1	yes	characteristic
155	C₇⋊D₇	—	2	4	no	—
156	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
157	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	2	yes	—
158	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	2	yes	—
159	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	3	yes	—
160	C₂×C₃×D₇	—	7	4	no	—
161	C₂×C₃×D₇	—	7	8	no	—
162	C₂×C₃×D₇	—	7	8	no	—
163	C₂×C₃×D₇	—	7	12	no	—
164	C₂×C₃×D₇	—	14	4	no	—
165	C₂×C₃×D₇	—	14	8	no	—
166	C₂×C₃×D₇	—	14	8	no	—
167	C₂×C₃×D₇	—	14	12	no	—
168	C₂²×ΓL(1,𝔽₈)	—	7	1	no	—
169	C₂²×ΓL(1,𝔽₈)	—	7	2	no	—
170	C₂²×ΓL(1,𝔽₈)	—	14	2	no	—
171	C₂²×ΓL(1,𝔽₈)	—	14	2	no	—
172	C₂²×ΓL(1,𝔽₈)	—	14	4	no	—
173	C₂²×ΓL(1,𝔽₈)	—	14	3	no	—
174	C₂²×ΓL(1,𝔽₈)	—	14	4	no	—
175	C₂²×ΓL(1,𝔽₈)	—	14	6	no	—
176	C₂×AGL(1,𝔽₇)	—	7	4	no	—
177	C₂×AGL(1,𝔽₇)	—	7	8	no	—
178	C₂×AGL(1,𝔽₇)	—	7	8	no	—
179	C₂×AGL(1,𝔽₇)	—	7	8	no	—
180	C₂×AGL(1,𝔽₇)	—	7	16	no	—
181	C₂×AGL(1,𝔽₇)	—	7	12	no	—
182	C₂×AGL(1,𝔽₇)	—	7	16	no	—
183	C₂×AGL(1,𝔽₇)	—	7	24	no	—
184	C₂×AGL(1,𝔽₇)	—	14	4	no	—
185	C₂×AGL(1,𝔽₇)	—	14	8	no	—
186	C₂×AGL(1,𝔽₇)	—	14	8	no	—
187	C₂×AGL(1,𝔽₇)	—	14	8	no	—
188	C₂×AGL(1,𝔽₇)	—	14	16	no	—
189	C₂×AGL(1,𝔽₇)	—	14	12	no	—
190	C₂×AGL(1,𝔽₇)	—	14	16	no	—
191	C₂×AGL(1,𝔽₇)	—	14	24	no	—
192	C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
193	C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	1	4	yes	complemented
194	C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	1	4	yes	complemented
195	C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	1	6	yes	complemented
196	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
197	C₄×ΓL(1,𝔽₈)	—	7	4	no	—
198	C₄×ΓL(1,𝔽₈)	—	14	4	no	—
199	C₄×ΓL(1,𝔽₈)	—	14	4	no	—
200	C₄×ΓL(1,𝔽₈)	—	14	8	no	—
201	C₄×ΓL(1,𝔽₈)	—	14	6	no	—
202	C₄×ΓL(1,𝔽₈)	—	14	8	no	—
203	C₄×ΓL(1,𝔽₈)	—	14	12	no	—
204	C₂³×C₃²	—	49	2	no	—
205	C₃²×D₄	—	49	4	no	—
206	C₂×C₃²×C₄	—	98	1	no	—
207	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
208	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
209	C₃×ΓL(1,𝔽₈)	—	14	2	no	—
210	C₃×ΓL(1,𝔽₈)	—	14	3	no	—
211	C₂²×D₇	—	7	2	no	—
212	C₂²×D₇	—	7	4	no	—
213	C₂²×D₇	—	7	4	no	—
214	C₂²×D₇	—	7	6	no	—
215	C₂×C₄×C₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
216	C₂×C₄×C₇	C₃×AGL(1,𝔽₇)	1	2	yes	complemented
217	C₂×C₄×C₇	C₃×AGL(1,𝔽₇)	1	2	yes	complemented
218	C₂×C₄×C₇	C₃×AGL(1,𝔽₇)	1	3	yes	complemented
219	D₂₈	—	7	4	no	—
220	D₂₈	—	7	8	no	—
221	D₂₈	—	7	8	no	—
222	D₂₈	—	7	12	no	—
223	C₇²	C₂×C₃²×D₄	1	1	yes	characteristic, complemented, Sylow
224	C₂×C₃×D₄	—	49	1	no	—
225	C₂×C₃×D₄	—	49	2	no	—
226	C₂×C₃×D₄	—	49	1	no	—
227	C₂×C₃×C₇	C₄⋊AGL(1,𝔽₇)	1	2	yes	complemented
228	C₂×C₃×C₇	C₄⋊AGL(1,𝔽₇)	1	4	yes	complemented
229	C₂×C₃×C₇	C₄⋊AGL(1,𝔽₇)	1	4	yes	complemented
230	C₂×C₃×C₇	C₄⋊AGL(1,𝔽₇)	1	6	yes	complemented
231	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
232	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	2	yes	—
233	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	2	yes	—
234	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	3	yes	—
235	C₃×D₇	—	14	4	no	—
236	C₃×D₇	—	14	8	no	—
237	C₃×D₇	—	14	8	no	—
238	C₃×D₇	—	14	12	no	—
239	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
240	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
241	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
242	C₂×ΓL(1,𝔽₈)	—	7	4	no	—
243	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
244	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
245	C₂×ΓL(1,𝔽₈)	—	14	4	no	—
246	C₂×ΓL(1,𝔽₈)	—	14	3	no	—
247	C₂×ΓL(1,𝔽₈)	—	14	4	no	—
248	C₂×ΓL(1,𝔽₈)	—	14	6	no	—
249	C₂×ΓL(1,𝔽₈)	—	14	4	no	—
250	C₂×ΓL(1,𝔽₈)	—	14	4	no	—
251	C₂×ΓL(1,𝔽₈)	—	14	8	no	—
252	C₂×ΓL(1,𝔽₈)	—	14	6	no	—
253	C₂×ΓL(1,𝔽₈)	—	14	8	no	—
254	C₂×ΓL(1,𝔽₈)	—	14	12	no	—
255	AGL(1,𝔽₇)	—	14	4	no	—
256	AGL(1,𝔽₇)	—	14	8	no	—
257	AGL(1,𝔽₇)	—	14	8	no	—
258	AGL(1,𝔽₇)	—	14	8	no	—
259	AGL(1,𝔽₇)	—	14	16	no	—
260	AGL(1,𝔽₇)	—	14	12	no	—
261	AGL(1,𝔽₇)	—	14	16	no	—
262	AGL(1,𝔽₇)	—	14	24	no	—
263	C₂²×C₃²	—	49	4	no	—
264	C₂²×C₃²	—	98	4	no	—
265	C₂²×C₃²	—	98	1	no	—
266	C₃²×C₄	—	98	2	no	—
267	C₂²×C₇	C₂×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
268	C₂²×C₇	C₂×C₃×AGL(1,𝔽₇)	1	2	yes	—
269	C₂²×C₇	C₂×C₃×AGL(1,𝔽₇)	1	2	yes	—
270	C₂²×C₇	C₂×C₃×AGL(1,𝔽₇)	1	3	yes	—
271	C₂×D₇	—	7	4	no	—
272	C₂×D₇	—	7	8	no	—
273	C₂×D₇	—	7	8	no	—
274	C₂×D₇	—	7	12	no	—
275	C₂×D₇	—	14	4	no	—
276	C₂×D₇	—	14	8	no	—
277	C₂×D₇	—	14	8	no	—
278	C₂×D₇	—	14	12	no	—
279	C₄×C₇	C₂×C₃×AGL(1,𝔽₇)	1	2	yes	complemented
280	C₄×C₇	C₂×C₃×AGL(1,𝔽₇)	1	4	yes	complemented
281	C₄×C₇	C₂×C₃×AGL(1,𝔽₇)	1	4	yes	complemented
282	C₄×C₇	C₂×C₃×AGL(1,𝔽₇)	1	6	yes	complemented
283	C₂³×C₃	—	49	2	no	—
284	C₂³×C₃	—	49	4	no	—
285	C₂³×C₃	—	49	2	no	—
286	C₃×D₄	—	49	4	no	—
287	C₃×D₄	—	49	8	no	—
288	C₃×D₄	—	49	4	no	—
289	C₂×C₃×C₄	—	98	1	no	—
290	C₂×C₃×C₄	—	98	2	no	—
291	C₂×C₃×C₄	#64424	1	1	yes	characteristic, complemented
292	C₃×C₇	C₂×C₄⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
293	C₃×C₇	C₂×C₄⋊AGL(1,𝔽₇)	1	2	yes	complemented
294	C₃×C₇	C₂×C₄⋊AGL(1,𝔽₇)	1	2	yes	complemented
295	C₃×C₇	C₂×C₄⋊AGL(1,𝔽₇)	1	3	yes	complemented
296	ΓL(1,𝔽₈)	—	7	1	no	—
297	ΓL(1,𝔽₈)	—	7	2	no	—
298	ΓL(1,𝔽₈)	—	14	2	no	—
299	ΓL(1,𝔽₈)	—	14	2	no	—
300	ΓL(1,𝔽₈)	—	14	4	no	—
301	ΓL(1,𝔽₈)	—	14	3	no	—
302	ΓL(1,𝔽₈)	—	14	4	no	—
303	ΓL(1,𝔽₈)	—	14	6	no	—
304	C₂×C₃²	—	98	4	no	—
305	C₂×C₃²	—	98	1	no	—
306	C₂×C₃²	—	98	2	no	—
307	C₂×D₄	—	49	1	no	Sylow
308	C₂×C₇	C₃×C₄⋊AGL(1,𝔽₇)	1	2	yes	complemented
309	C₂×C₇	C₃×C₄⋊AGL(1,𝔽₇)	1	4	yes	complemented
310	C₂×C₇	C₃×C₄⋊AGL(1,𝔽₇)	1	4	yes	complemented
311	C₂×C₇	C₃×C₄⋊AGL(1,𝔽₇)	1	6	yes	complemented
312	C₂×C₇	C₂²×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
313	C₂×C₇	C₂²×C₃×AGL(1,𝔽₇)	1	2	yes	—
314	C₂×C₇	C₂²×C₃×AGL(1,𝔽₇)	1	2	yes	—
315	C₂×C₇	C₂²×C₃×AGL(1,𝔽₇)	1	3	yes	—
316	D₇	—	14	4	no	—
317	D₇	—	14	8	no	—
318	D₇	—	14	8	no	—
319	D₇	—	14	12	no	—
320	C₂²×C₃	—	49	4	no	—
321	C₂²×C₃	—	49	8	no	—
322	C₂²×C₃	—	49	4	no	—
323	C₂²×C₃	—	98	4	no	—
324	C₂²×C₃	—	98	8	no	—
325	C₂²×C₃	—	98	4	no	—
326	C₂²×C₃	—	98	1	no	—
327	C₂²×C₃	—	98	2	no	—
328	C₂²×C₃	C₂×#64424	1	1	yes	characteristic
329	C₃×C₄	—	98	2	no	—
330	C₃×C₄	—	98	4	no	—
331	C₃×C₄	C₂×#64424	1	2	yes	complemented
332	C₃²	—	98	1	no	Sylow
333	C₂³	—	49	2	no	—
334	D₄	—	49	4	no	—
335	C₂×C₄	C₃×#64424	1	1	yes	characteristic, complemented
336	C₇	C₂×C₃×C₄⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
337	C₇	C₂×C₃×C₄⋊AGL(1,𝔽₇)	1	2	yes	complemented
338	C₇	C₂×C₃×C₄⋊AGL(1,𝔽₇)	1	2	yes	complemented
339	C₇	C₂×C₃×C₄⋊AGL(1,𝔽₇)	1	3	yes	complemented
340	C₂×C₃	—	98	4	no	—
341	C₂×C₃	—	98	8	no	—
342	C₂×C₃	—	98	4	no	—
343	C₂×C₃	—	98	1	no	—
344	C₂×C₃	—	98	2	no	—
345	C₂×C₃	—	98	2	no	—
346	C₂×C₃	—	98	4	no	—
347	C₂×C₃	C₄⋊#64424	1	2	yes	direct product factor
348	C₂×C₃	C₂²×#64424	1	1	yes	characteristic
349	C₂²	—	49	4	no	—
350	C₂²	—	98	4	no	—
351	C₂²	C₂×C₃×#64424	1	1	yes	characteristic
352	C₄	C₂×C₃×#64424	1	2	yes	complemented
353	C₃	—	98	1	no	—
354	C₃	—	98	2	no	—
355	C₃	C₂×C₄⋊#64424	1	1	yes	characteristic, direct product factor
356	C₂	—	98	4	no	—
357	C₂	C₂²×C₃×#64424	1	1	yes	characteristic
358	C₂	C₃×C₄⋊#64424	1	2	yes	direct product factor

	subgroup	G/H
center	C₂²×C₃	C₂×#64424
commutator, cosocle	C₂×C₇²	C₂³×C₃²
Frattini	C₂	C₂²×C₃×#64424
Fitting	C₂×C₃×C₄×C₇²	C₂×C₃
socle	C₂²×C₃×C₇²	C₂²×C₃
hypercenter	C₂×C₃×C₄	#64424
hypocenter	C₇²	C₂×C₃²×D₄
LCS	G ▷ C₂×C₇² ▷ C₇²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₃×C₄⋊#64424	C₂	direct (N × H)
2. C₂×C₃×C₄×#3861	C₂	semidirect
3. C₂×C₃×C₄⋊(C₇⋊D₇)	C₃	semidirect
4. C₂²×C₃×#64424	C₂	semidirect
5. C₂×C₄⋊#64424	C₃	direct (N × H)
6. C₂×C₄⋊#64424	C₃	direct (N × H)
9. C₂×C₃×#64424	C₂²	semidirect
10. C₃×C₄×#3861	C₂²	semidirect
11. C₂²×C₃×C₇⋊D₇	C₂×C₃	semidirect
12. C₂²×#64424	C₂×C₃	semidirect
13. C₂²×#64424	C₂×C₃	semidirect
14. C₂×C₃×C₄×C₇²	C₂×C₃	semidirect
15. C₃×C₄⋊(C₇⋊D₇)	C₂×C₃	semidirect
16. C₂×C₄×#3861	C₂×C₃	semidirect
17. C₂×C₄×#3861	C₂×C₃	semidirect
18. C₄⋊#64424	C₂×C₃	direct (N × H)
19. C₄⋊#64424	C₂×C₃	direct (N × H)
24. C₂×C₃×#3861	D₄	semidirect
27. C₂×C₄⋊(C₇⋊D₇)	C₃²	semidirect
30. C₂×C₃×C₇⋊D₇	C₂²×C₃	semidirect
35. C₂×#64424	C₂²×C₃	semidirect
36. C₂×#64424	C₂²×C₃	semidirect
37. C₃×C₄×C₇²	C₂²×C₃	semidirect
38. C₄×#3861	C₂²×C₃	semidirect
39. C₄×#3861	C₂²×C₃	semidirect
52. C₃×#3861	C₂×D₄	semidirect
53. C₂²×C₇⋊D₇	C₂×C₃²	semidirect
54. C₂×C₄×C₇²	C₂×C₃²	semidirect
55. C₄⋊(C₇⋊D₇)	C₂×C₃²	semidirect
68. C₂×C₃×C₇²	C₃×D₄	semidirect
71. C₂×#3861	C₃×D₄	semidirect
72. C₂×#3861	C₃×D₄	semidirect
95. C₂×C₇⋊D₇	C₂²×C₃²	semidirect
96. C₄×C₇²	C₂²×C₃²	semidirect
109. C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	semidirect
110. C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	semidirect
111. C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	semidirect
112. C₂×C₃×C₄×C₇	AGL(1,𝔽₇)	semidirect
133. C₃×C₇²	C₂×C₃×D₄	semidirect
134. #3861	C₂×C₃×D₄	semidirect
135. #3861	C₂×C₃×D₄	semidirect
153. C₂×C₇²	C₃²×D₄	semidirect
192. C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
193. C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
194. C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
195. C₃×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
215. C₂×C₄×C₇	C₃×AGL(1,𝔽₇)	semidirect
216. C₂×C₄×C₇	C₃×AGL(1,𝔽₇)	semidirect
217. C₂×C₄×C₇	C₃×AGL(1,𝔽₇)	semidirect
218. C₂×C₄×C₇	C₃×AGL(1,𝔽₇)	semidirect
223. C₇²	C₂×C₃²×D₄	semidirect
227. C₂×C₃×C₇	C₄⋊AGL(1,𝔽₇)	semidirect
228. C₂×C₃×C₇	C₄⋊AGL(1,𝔽₇)	semidirect
229. C₂×C₃×C₇	C₄⋊AGL(1,𝔽₇)	semidirect
230. C₂×C₃×C₇	C₄⋊AGL(1,𝔽₇)	semidirect
279. C₄×C₇	C₂×C₃×AGL(1,𝔽₇)	semidirect
280. C₄×C₇	C₂×C₃×AGL(1,𝔽₇)	semidirect
281. C₄×C₇	C₂×C₃×AGL(1,𝔽₇)	semidirect
282. C₄×C₇	C₂×C₃×AGL(1,𝔽₇)	semidirect
291. C₂×C₃×C₄	#64424	semidirect
292. C₃×C₇	C₂×C₄⋊AGL(1,𝔽₇)	semidirect
293. C₃×C₇	C₂×C₄⋊AGL(1,𝔽₇)	semidirect
294. C₃×C₇	C₂×C₄⋊AGL(1,𝔽₇)	semidirect
295. C₃×C₇	C₂×C₄⋊AGL(1,𝔽₇)	semidirect
308. C₂×C₇	C₃×C₄⋊AGL(1,𝔽₇)	semidirect
309. C₂×C₇	C₃×C₄⋊AGL(1,𝔽₇)	semidirect
310. C₂×C₇	C₃×C₄⋊AGL(1,𝔽₇)	semidirect
311. C₂×C₇	C₃×C₄⋊AGL(1,𝔽₇)	semidirect
331. C₃×C₄	C₂×#64424	semidirect
335. C₂×C₄	C₃×#64424	semidirect
336. C₇	C₂×C₃×C₄⋊AGL(1,𝔽₇)	semidirect
337. C₇	C₂×C₃×C₄⋊AGL(1,𝔽₇)	semidirect
338. C₇	C₂×C₃×C₄⋊AGL(1,𝔽₇)	semidirect
339. C₇	C₂×C₃×C₄⋊AGL(1,𝔽₇)	semidirect
347. C₂×C₃	C₄⋊#64424	direct (N × H)
352. C₄	C₂×C₃×#64424	semidirect
355. C₃	C₂×C₄⋊#64424	direct (N × H)
358. C₂	C₃×C₄⋊#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
C₃×C₄⋊#64424	2
C₂×C₃×C₄×#3861	2
C₂×C₃×C₄⋊(C₇⋊D₇)	3
C₂²×C₃×#64424	2
C₂×C₄⋊#64424	3
C₂×C₃×C₄⋊AGL(1,𝔽₇)	7

Subgroups — C2×C3×C4⋊#64424 #72245988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄⋊#64424 #72245988