Subgroups — C₂×C₃×#11924207 #72246499

Order 7056.

936 conjugacy classes of subgroups.

The subgroup lattice has 370 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	C₂²×C₃×#64423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₇×C₂²⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₃×#3861	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#11924207	C₂	1	4	yes	maximal, direct product factor
6	C₂×#11924207	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×#11924207	C₃	1	2	yes	maximal, direct product factor
8	C₂²×C₃×#3861	—	2	2	no	—
9	C₂²×C₃×#3861	C₂²	1	1	yes	characteristic
10	C₂²×C₃×#3861	C₂²	1	2	yes	complemented
11	C₂×C₃×#64423	—	2	2	no	—
12	C₂×C₃×#64423	C₂²	1	2	yes	complemented
13	C₃×#10596873	C₂²	1	2	yes	complemented
14	C₂³×C₃×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₇×D₇	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂³×#3861	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂³×#3861	C₂×C₃	1	2	yes	complemented
18	C₂²×#64423	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂²×#64423	C₂×C₃	1	2	yes	complemented
20	C₃×C₇×C₂²⋊D₇	C₂×C₃	1	4	yes	complemented
21	C₂×C₃×C₇×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
22	#11924207	C₂×C₃	1	4	yes	direct product factor
23	#11924207	C₂×C₃	1	8	yes	direct product factor
24	C₂×#10596873	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#10596873	C₂×C₃	1	2	yes	complemented
26	C₂×C₃×D₄×ΓL(1,𝔽₈)	—	7	1	no	maximal
27	C₂×C₃×(C₂²⋊D₇)⋊C₃	—	7	1	no	maximal
28	C₂×C₃×#3861	—	2	2	no	—
29	C₂×C₃×#3861	D₄	1	2	yes	complemented
30	C₂×C₃×#3861	C₂³	1	1	yes	characteristic
31	C₃×#64423	—	2	2	no	—
32	C₂×C₇×C₂²⋊D₇	C₃²	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₃×C₇²	—	2	2	no	—
34	C₂²×C₃×C₇²	C₂²×C₃	1	1	yes	characteristic
35	C₂²×C₃×C₇²	C₂²×C₃	1	2	yes	complemented
36	C₂×C₃×C₇×D₇	—	2	2	no	—
37	C₂×C₃×C₇×D₇	C₂²×C₃	1	2	yes	complemented
38	C₂²×#3861	—	2	2	no	—
39	C₂²×#3861	—	2	4	no	—
40	C₂²×#3861	C₂²×C₃	1	1	yes	characteristic
41	C₂²×#3861	C₂²×C₃	1	2	yes	—
42	C₂²×#3861	C₂²×C₃	1	2	yes	complemented
43	C₂²×#3861	C₂²×C₃	1	4	yes	complemented
44	C₂×#64423	—	2	2	no	—
45	C₂×#64423	—	2	4	no	—
46	C₂×#64423	C₂²×C₃	1	2	yes	complemented
47	C₂×#64423	C₂²×C₃	1	4	yes	complemented
48	C₃×C₇×Dic₇	C₂²×C₃	1	2	yes	complemented
49	#10596873	C₂²×C₃	1	2	yes	complemented
50	#10596873	C₂²×C₃	1	4	yes	complemented
51	C₂³×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
52	C₂³×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
53	C₂³×C₃×ΓL(1,𝔽₈)	—	14	3	no	—
54	C₂³×C₃×ΓL(1,𝔽₈)	—	14	1	no	—
55	C₂²×C₃×AGL(1,𝔽₇)	—	7	1	no	—
56	C₃×D₄×ΓL(1,𝔽₈)	—	7	4	no	—
57	C₂×C₃×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
58	C₃×(C₂²⋊D₇)⋊C₃	—	7	4	no	—
59	C₂×C₃×ΓL(1,𝔽₈)⋊C₄	—	7	1	no	—
60	C₃×#3861	C₂×D₄	1	1	yes	characteristic, complemented, Hall
61	C₂³×C₇²	C₂×C₃²	1	1	yes	characteristic, complemented
62	C₂²×C₇×D₇	C₂×C₃²	1	1	yes	characteristic, complemented
63	C₇×C₂²⋊D₇	C₂×C₃²	1	4	yes	complemented
64	C₂×C₇×Dic₇	C₂×C₃²	1	1	yes	characteristic, complemented
65	C₂×C₃×C₇×D₄	—	7	1	no	—
66	C₂×C₃×C₂²⋊D₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
67	C₂×D₄×ΓL(1,𝔽₈)	—	7	1	no	—
68	C₂×D₄×ΓL(1,𝔽₈)	—	7	2	no	—
69	C₂×(C₂²⋊D₇)⋊C₃	—	7	1	no	—
70	C₂×(C₂²⋊D₇)⋊C₃	—	7	2	no	—
71	C₂×C₃×C₇²	—	2	2	no	—
72	C₂×C₃×C₇²	C₃×D₄	1	2	yes	complemented
73	C₂×C₃×C₇²	C₂³×C₃	1	1	yes	characteristic
74	C₃×C₇×D₇	—	2	2	no	—
75	C₂×#3861	—	2	2	no	—
76	C₂×#3861	—	2	4	no	—
77	C₂×#3861	C₃×D₄	1	2	yes	complemented
78	C₂×#3861	C₃×D₄	1	4	yes	complemented
79	C₂×#3861	C₂³×C₃	1	1	yes	characteristic
80	C₂×#3861	C₂³×C₃	1	2	yes	—
81	#64423	—	2	2	no	—
82	#64423	—	2	4	no	—
83	C₂²×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
84	C₂²×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
85	C₂²×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
86	C₂²×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
87	C₂²×C₃×ΓL(1,𝔽₈)	—	14	6	no	—
88	C₂²×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
89	C₂²×C₃×ΓL(1,𝔽₈)	—	14	3	no	—
90	C₂²×C₃×ΓL(1,𝔽₈)	—	14	6	no	—
91	C₂²×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
92	C₂²×C₃×ΓL(1,𝔽₈)	—	14	1	no	—
93	C₂²×C₃×ΓL(1,𝔽₈)	—	14	6	no	—
94	C₂²×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
95	C₂×C₃×AGL(1,𝔽₇)	—	7	2	no	—
96	C₂×C₃×AGL(1,𝔽₇)	—	14	2	no	—
97	C₃×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
98	C₃×ΓL(1,𝔽₈)⋊C₄	—	7	2	no	—
99	C₂²×C₇²	—	2	2	no	—
100	C₂²×C₇²	C₂²×C₃²	1	1	yes	characteristic
101	C₂²×C₇²	C₂²×C₃²	1	2	yes	complemented
102	C₂×C₇×D₇	—	2	2	no	—
103	C₂×C₇×D₇	C₂²×C₃²	1	2	yes	complemented
104	C₇×Dic₇	C₂²×C₃²	1	2	yes	complemented
105	C₂³×C₃×C₇	—	2	3	no	—
106	C₂³×C₃×C₇	—	7	1	no	—
107	C₂³×C₃×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
108	C₂³×C₃×C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
109	C₂²×C₃×D₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
110	C₂³×ΓL(1,𝔽₈)	—	7	1	no	—
111	C₂³×ΓL(1,𝔽₈)	—	7	2	no	—
112	C₂³×ΓL(1,𝔽₈)	—	7	1	no	—
113	C₂³×ΓL(1,𝔽₈)	—	7	2	no	—
114	C₂³×ΓL(1,𝔽₈)	—	14	3	no	—
115	C₂³×ΓL(1,𝔽₈)	—	14	6	no	—
116	C₂³×ΓL(1,𝔽₈)	—	14	1	no	—
117	C₂³×ΓL(1,𝔽₈)	—	14	2	no	—
118	C₂²×AGL(1,𝔽₇)	—	7	1	no	—
119	C₂²×AGL(1,𝔽₇)	—	7	2	no	—
120	C₃×C₇×D₄	—	7	4	no	—
121	C₂×C₃×C₄×C₇	—	7	1	no	—
122	C₃×C₂²⋊D₇	C₂×ΓL(1,𝔽₈)	1	4	yes	complemented
123	C₂×C₃×Dic₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
124	D₄×ΓL(1,𝔽₈)	—	7	4	no	—
125	D₄×ΓL(1,𝔽₈)	—	7	8	no	—
126	C₂×C₄×ΓL(1,𝔽₈)	—	7	1	no	—
127	C₂×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
128	(C₂²⋊D₇)⋊C₃	—	7	4	no	—
129	(C₂²⋊D₇)⋊C₃	—	7	8	no	—
130	C₂×ΓL(1,𝔽₈)⋊C₄	—	7	1	no	—
131	C₂×ΓL(1,𝔽₈)⋊C₄	—	7	2	no	—
132	C₃×C₇²	C₂×C₃×D₄	1	1	yes	characteristic, complemented
133	#3861	C₂×C₃×D₄	1	1	yes	characteristic, complemented
134	#3861	C₂×C₃×D₄	1	2	yes	complemented
135	C₂×C₃²×D₄	—	49	1	no	Hall
136	C₂×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
137	C₂×C₃×ΓL(1,𝔽₈)	—	7	1	no	—
138	C₂×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
139	C₂×C₃×ΓL(1,𝔽₈)	—	14	6	no	—
140	C₂×C₃×ΓL(1,𝔽₈)	—	14	6	no	—
141	C₂×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
142	C₂×C₃×ΓL(1,𝔽₈)	—	14	6	no	—
143	C₂×C₃×ΓL(1,𝔽₈)	—	14	3	no	—
144	C₂×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
145	C₂×C₃×ΓL(1,𝔽₈)	—	14	2	no	—
146	C₂×C₃×ΓL(1,𝔽₈)	—	14	1	no	—
147	C₃×AGL(1,𝔽₇)	—	14	2	no	—
148	C₂×C₇×D₄	—	7	1	no	—
149	C₂×C₂²⋊D₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
150	C₂×C₇²	—	2	2	no	—
151	C₂×C₇²	C₃²×D₄	1	2	yes	complemented
152	C₂×C₇²	C₂³×C₃²	1	1	yes	characteristic
153	C₇×D₇	—	2	2	no	—
154	C₂²×C₃×C₇	—	2	6	no	—
155	C₂²×C₃×C₇	—	2	6	no	—
156	C₂²×C₃×C₇	—	2	2	no	—
157	C₂²×C₃×C₇	—	2	2	no	—
158	C₂²×C₃×C₇	—	2	3	no	—
159	C₂²×C₃×C₇	—	2	6	no	—
160	C₂²×C₃×C₇	—	7	2	no	—
161	C₂²×C₃×C₇	—	14	2	no	—
162	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
163	C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
164	C₂²×C₃×C₇	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
165	C₂²×C₃×C₇	C₂²×ΓL(1,𝔽₈)	1	2	yes	complemented
166	C₂×C₃×D₇	—	2	2	no	—
167	C₂×C₃×D₇	C₂²×ΓL(1,𝔽₈)	1	2	yes	complemented
168	C₂²×ΓL(1,𝔽₈)	—	7	2	no	—
169	C₂²×ΓL(1,𝔽₈)	—	7	4	no	—
170	C₂²×ΓL(1,𝔽₈)	—	7	1	no	—
171	C₂²×ΓL(1,𝔽₈)	—	7	2	no	—
172	C₂²×ΓL(1,𝔽₈)	—	7	2	no	—
173	C₂²×ΓL(1,𝔽₈)	—	7	4	no	—
174	C₂²×ΓL(1,𝔽₈)	—	14	6	no	—
175	C₂²×ΓL(1,𝔽₈)	—	14	3	no	—
176	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
177	C₂²×ΓL(1,𝔽₈)	—	14	2	no	—
178	C₂²×ΓL(1,𝔽₈)	—	14	2	no	—
179	C₂²×ΓL(1,𝔽₈)	—	14	4	no	—
180	C₂²×ΓL(1,𝔽₈)	—	14	12	no	—
181	C₂²×ΓL(1,𝔽₈)	—	14	6	no	—
182	C₂²×ΓL(1,𝔽₈)	—	14	12	no	—
183	C₂²×ΓL(1,𝔽₈)	—	14	6	no	—
184	C₂²×ΓL(1,𝔽₈)	—	14	2	no	—
185	C₂²×ΓL(1,𝔽₈)	—	14	12	no	—
186	C₂²×ΓL(1,𝔽₈)	—	14	4	no	—
187	C₂²×ΓL(1,𝔽₈)	—	14	6	no	—
188	C₂²×ΓL(1,𝔽₈)	—	14	2	no	—
189	C₂²×ΓL(1,𝔽₈)	—	14	4	no	—
190	C₂²×ΓL(1,𝔽₈)	—	14	2	no	—
191	C₂²×ΓL(1,𝔽₈)	—	14	4	no	—
192	C₂×AGL(1,𝔽₇)	—	7	2	no	—
193	C₂×AGL(1,𝔽₇)	—	7	4	no	—
194	C₂×AGL(1,𝔽₇)	—	14	2	no	—
195	C₂×AGL(1,𝔽₇)	—	14	4	no	—
196	C₃×C₄×C₇	—	7	2	no	—
197	C₃×Dic₇	C₂²×ΓL(1,𝔽₈)	1	2	yes	complemented
198	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
199	C₄×ΓL(1,𝔽₈)	—	7	4	no	—
200	ΓL(1,𝔽₈)⋊C₄	—	7	2	no	—
201	ΓL(1,𝔽₈)⋊C₄	—	7	4	no	—
202	C₂³×C₃²	—	49	1	no	—
203	C₂³×C₃²	—	98	1	no	—
204	C₃²×D₄	—	49	4	no	—
205	C₂×C₃²×C₄	—	49	1	no	—
206	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
207	C₃×ΓL(1,𝔽₈)	—	14	3	no	—
208	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
209	C₂³×C₇	—	2	3	no	—
210	C₂³×C₇	—	7	1	no	—
211	C₂³×C₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
212	C₂³×C₇	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
213	C₂²×D₇	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
214	C₇×D₄	—	7	4	no	—
215	C₂×C₄×C₇	—	7	1	no	—
216	C₂²⋊D₇	C₂×C₃×ΓL(1,𝔽₈)	1	4	yes	complemented
217	C₂×Dic₇	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
218	C₇²	C₂×C₃²×D₄	1	1	yes	characteristic, complemented, Sylow
219	C₂×C₃×D₄	—	7	1	no	—
220	C₂×C₃×D₄	—	49	1	no	—
221	C₂×C₃×D₄	—	49	2	no	—
222	C₂×C₃×C₇	—	2	6	no	—
223	C₂×C₃×C₇	—	2	6	no	—
224	C₂×C₃×C₇	—	2	2	no	—
225	C₂×C₃×C₇	—	2	2	no	—
226	C₂×C₃×C₇	—	2	3	no	—
227	C₂×C₃×C₇	—	2	6	no	—
228	C₂×C₃×C₇	—	14	2	no	—
229	C₂×C₃×C₇	(C₂²⋊D₇)⋊C₃	1	2	yes	complemented
230	C₂×C₃×C₇	D₄×ΓL(1,𝔽₈)	1	2	yes	complemented
231	C₂×C₃×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
232	C₂×C₃×C₇	C₂³×ΓL(1,𝔽₈)	1	1	yes	characteristic
233	C₃×D₇	—	2	2	no	—
234	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
235	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
236	C₂×ΓL(1,𝔽₈)	—	7	4	no	—
237	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
238	C₂×ΓL(1,𝔽₈)	—	14	6	no	—
239	C₂×ΓL(1,𝔽₈)	—	14	3	no	—
240	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
241	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
242	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
243	C₂×ΓL(1,𝔽₈)	—	14	4	no	—
244	C₂×ΓL(1,𝔽₈)	—	14	6	no	—
245	C₂×ΓL(1,𝔽₈)	—	14	12	no	—
246	C₂×ΓL(1,𝔽₈)	—	14	6	no	—
247	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
248	C₂×ΓL(1,𝔽₈)	—	14	12	no	—
249	C₂×ΓL(1,𝔽₈)	—	14	4	no	—
250	C₂×ΓL(1,𝔽₈)	—	14	12	no	—
251	C₂×ΓL(1,𝔽₈)	—	14	6	no	—
252	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
253	C₂×ΓL(1,𝔽₈)	—	14	4	no	—
254	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
255	C₂×ΓL(1,𝔽₈)	—	14	4	no	—
256	AGL(1,𝔽₇)	—	14	2	no	—
257	AGL(1,𝔽₇)	—	14	4	no	—
258	C₂²×C₃²	—	49	2	no	—
259	C₂²×C₃²	—	98	2	no	—
260	C₂²×C₃²	—	98	2	no	—
261	C₂²×C₃²	—	98	1	no	—
262	C₂²×C₃²	—	98	2	no	—
263	C₃²×C₄	—	49	2	no	—
264	C₂²×C₇	—	2	6	no	—
265	C₂²×C₇	—	2	6	no	—
266	C₂²×C₇	—	2	2	no	—
267	C₂²×C₇	—	2	2	no	—
268	C₂²×C₇	—	2	3	no	—
269	C₂²×C₇	—	2	6	no	—
270	C₂²×C₇	—	7	2	no	—
271	C₂²×C₇	—	14	2	no	—
272	C₂²×C₇	C₂×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
273	C₂²×C₇	C₂×C₃×AGL(1,𝔽₇)	1	2	yes	complemented
274	C₂²×C₇	C₂²×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
275	C₂²×C₇	C₂²×C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
276	C₂×D₇	—	2	2	no	—
277	C₂×D₇	C₂²×C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
278	C₄×C₇	—	7	2	no	—
279	Dic₇	C₂²×C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
280	C₂³×C₃	—	7	1	no	—
281	C₂³×C₃	—	49	1	no	—
282	C₂³×C₃	—	49	2	no	—
283	C₂³×C₃	—	49	1	no	—
284	C₂³×C₃	—	98	2	no	—
285	C₂³×C₃	#64423	1	1	yes	characteristic, complemented
286	C₃×D₄	—	7	4	no	—
287	C₃×D₄	—	49	4	no	—
288	C₃×D₄	—	49	8	no	—
289	C₂×C₃×C₄	—	7	1	no	—
290	C₂×C₃×C₄	—	49	1	no	—
291	C₂×C₃×C₄	—	49	2	no	—
292	C₃×C₇	—	2	3	no	—
293	C₃×C₇	C₂×(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic, complemented
294	C₃×C₇	C₂×D₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
295	ΓL(1,𝔽₈)	—	7	1	no	—
296	ΓL(1,𝔽₈)	—	7	2	no	—
297	ΓL(1,𝔽₈)	—	14	3	no	—
298	ΓL(1,𝔽₈)	—	14	1	no	—
299	ΓL(1,𝔽₈)	—	14	6	no	—
300	ΓL(1,𝔽₈)	—	14	2	no	—
301	C₂×C₃²	—	98	2	no	—
302	C₂×C₃²	—	98	2	no	—
303	C₂×C₃²	—	98	1	no	—
304	C₂×C₃²	—	98	2	no	—
305	C₂×D₄	—	7	1	no	Sylow
306	C₂×C₇	—	2	6	no	—
307	C₂×C₇	—	2	6	no	—
308	C₂×C₇	—	2	2	no	—
309	C₂×C₇	—	2	2	no	—
310	C₂×C₇	—	2	6	no	—
311	C₂×C₇	—	2	3	no	—
312	C₂×C₇	—	14	2	no	—
313	C₂×C₇	C₃×(C₂²⋊D₇)⋊C₃	1	2	yes	complemented
314	C₂×C₇	C₃×D₄×ΓL(1,𝔽₈)	1	2	yes	complemented
315	C₂×C₇	C₂²×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
316	C₂×C₇	C₂³×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
317	D₇	—	2	2	no	—
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	7	2	no	—
320	C₂²×C₃	—	14	2	no	—
321	C₂²×C₃	—	49	2	no	—
322	C₂²×C₃	—	49	4	no	—
323	C₂²×C₃	—	49	1	no	—
324	C₂²×C₃	—	49	2	no	—
325	C₂²×C₃	—	98	2	no	—
326	C₂²×C₃	—	98	4	no	—
327	C₂²×C₃	—	98	2	no	—
328	C₂²×C₃	—	98	4	no	—
329	C₂²×C₃	—	98	2	no	—
330	C₂²×C₃	—	98	4	no	—
331	C₂²×C₃	C₂×#64423	1	1	yes	characteristic
332	C₂²×C₃	C₂×#64423	1	2	yes	complemented
333	C₃×C₄	—	7	2	no	—
334	C₃×C₄	—	49	2	no	—
335	C₃×C₄	—	49	4	no	—
336	C₃²	—	98	1	no	Sylow
337	C₂³	—	7	1	no	—
338	C₂³	C₃×#64423	1	1	yes	characteristic, complemented
339	D₄	—	7	4	no	—
340	C₂×C₄	—	7	1	no	—
341	C₇	—	2	3	no	—
342	C₇	C₂×C₃×(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic, complemented
343	C₇	C₂×C₃×D₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
344	C₂×C₃	—	2	2	no	—
345	C₂×C₃	—	14	2	no	—
346	C₂×C₃	—	49	2	no	—
347	C₂×C₃	—	49	1	no	—
348	C₂×C₃	—	98	2	no	—
349	C₂×C₃	—	98	4	no	—
350	C₂×C₃	—	98	2	no	—
351	C₂×C₃	—	98	4	no	—
352	C₂×C₃	—	98	4	no	—
353	C₂×C₃	—	98	2	no	—
354	C₂×C₃	#11924207	1	2	yes	direct product factor
355	C₂×C₃	C₂²×#64423	1	1	yes	characteristic
356	C₂²	—	2	2	no	—
357	C₂²	—	7	2	no	—
358	C₂²	—	14	2	no	—
359	C₂²	C₂×C₃×#64423	1	1	yes	characteristic
360	C₂²	C₂×C₃×#64423	1	2	yes	complemented
361	C₄	—	7	2	no	—
362	C₃	—	49	1	no	—
363	C₃	—	98	2	no	—
364	C₃	C₂×#11924207	1	1	yes	characteristic, direct product factor
365	C₂	—	2	2	no	—
366	C₂	—	14	2	no	—
367	C₂	C₃×#11924207	1	2	yes	direct product factor
368	C₂	C₂²×C₃×#64423	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#64423
commutator, cosocle	C₂×C₇²	C₂³×C₃²
Frattini	C₂	C₂²×C₃×#64423
Fitting	C₂³×C₃×C₇²	C₂×C₃
socle	C₂²×C₃×C₇²	C₂²×C₃
hypercenter	C₂³×C₃	#64423
hypocenter	C₇²	C₂×C₃²×D₄
LCS	G ▷ C₂×C₇² ▷ C₇²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂³×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#10596873	C₂	semidirect
2. C₂²×C₃×#64423	C₂	semidirect
3. C₂×C₃×C₇×C₂²⋊D₇	C₃	semidirect
4. C₂³×C₃×#3861	C₂	semidirect
5. C₃×#11924207	C₂	direct (N × H)
6. C₂×#11924207	C₃	direct (N × H)
7. C₂×#11924207	C₃	direct (N × H)
10. C₂²×C₃×#3861	C₂²	semidirect
12. C₂×C₃×#64423	C₂²	semidirect
13. C₃×#10596873	C₂²	semidirect
14. C₂³×C₃×C₇²	C₂×C₃	semidirect
15. C₂²×C₃×C₇×D₇	C₂×C₃	semidirect
16. C₂³×#3861	C₂×C₃	semidirect
17. C₂³×#3861	C₂×C₃	semidirect
18. C₂²×#64423	C₂×C₃	semidirect
19. C₂²×#64423	C₂×C₃	semidirect
20. C₃×C₇×C₂²⋊D₇	C₂×C₃	semidirect
21. C₂×C₃×C₇×Dic₇	C₂×C₃	semidirect
22. #11924207	C₂×C₃	direct (N × H)
23. #11924207	C₂×C₃	direct (N × H)
24. C₂×#10596873	C₂×C₃	semidirect
25. C₂×#10596873	C₂×C₃	semidirect
29. C₂×C₃×#3861	D₄	semidirect
32. C₂×C₇×C₂²⋊D₇	C₃²	semidirect
35. C₂²×C₃×C₇²	C₂²×C₃	semidirect
37. C₂×C₃×C₇×D₇	C₂²×C₃	semidirect
42. C₂²×#3861	C₂²×C₃	semidirect
43. C₂²×#3861	C₂²×C₃	semidirect
46. C₂×#64423	C₂²×C₃	semidirect
47. C₂×#64423	C₂²×C₃	semidirect
48. C₃×C₇×Dic₇	C₂²×C₃	semidirect
49. #10596873	C₂²×C₃	semidirect
50. #10596873	C₂²×C₃	semidirect
60. C₃×#3861	C₂×D₄	semidirect
61. C₂³×C₇²	C₂×C₃²	semidirect
62. C₂²×C₇×D₇	C₂×C₃²	semidirect
63. C₇×C₂²⋊D₇	C₂×C₃²	semidirect
64. C₂×C₇×Dic₇	C₂×C₃²	semidirect
66. C₂×C₃×C₂²⋊D₇	ΓL(1,𝔽₈)	semidirect
72. C₂×C₃×C₇²	C₃×D₄	semidirect
77. C₂×#3861	C₃×D₄	semidirect
78. C₂×#3861	C₃×D₄	semidirect
101. C₂²×C₇²	C₂²×C₃²	semidirect
103. C₂×C₇×D₇	C₂²×C₃²	semidirect
104. C₇×Dic₇	C₂²×C₃²	semidirect
107. C₂³×C₃×C₇	AGL(1,𝔽₇)	semidirect
108. C₂³×C₃×C₇	C₂×ΓL(1,𝔽₈)	semidirect
109. C₂²×C₃×D₇	C₂×ΓL(1,𝔽₈)	semidirect
122. C₃×C₂²⋊D₇	C₂×ΓL(1,𝔽₈)	semidirect
123. C₂×C₃×Dic₇	C₂×ΓL(1,𝔽₈)	semidirect
132. C₃×C₇²	C₂×C₃×D₄	semidirect
133. #3861	C₂×C₃×D₄	semidirect
134. #3861	C₂×C₃×D₄	semidirect
149. C₂×C₂²⋊D₇	C₃×ΓL(1,𝔽₈)	semidirect
151. C₂×C₇²	C₃²×D₄	semidirect
163. C₂²×C₃×C₇	C₂×AGL(1,𝔽₇)	semidirect
165. C₂²×C₃×C₇	C₂²×ΓL(1,𝔽₈)	semidirect
167. C₂×C₃×D₇	C₂²×ΓL(1,𝔽₈)	semidirect
197. C₃×Dic₇	C₂²×ΓL(1,𝔽₈)	semidirect
211. C₂³×C₇	C₃×AGL(1,𝔽₇)	semidirect
212. C₂³×C₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
213. C₂²×D₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
216. C₂²⋊D₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
217. C₂×Dic₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
218. C₇²	C₂×C₃²×D₄	semidirect
229. C₂×C₃×C₇	(C₂²⋊D₇)⋊C₃	semidirect
230. C₂×C₃×C₇	D₄×ΓL(1,𝔽₈)	semidirect
273. C₂²×C₇	C₂×C₃×AGL(1,𝔽₇)	semidirect
275. C₂²×C₇	C₂²×C₃×ΓL(1,𝔽₈)	semidirect
277. C₂×D₇	C₂²×C₃×ΓL(1,𝔽₈)	semidirect
279. Dic₇	C₂²×C₃×ΓL(1,𝔽₈)	semidirect
285. C₂³×C₃	#64423	semidirect
293. C₃×C₇	C₂×(C₂²⋊D₇)⋊C₃	semidirect
294. C₃×C₇	C₂×D₄×ΓL(1,𝔽₈)	semidirect
313. C₂×C₇	C₃×(C₂²⋊D₇)⋊C₃	semidirect
314. C₂×C₇	C₃×D₄×ΓL(1,𝔽₈)	semidirect
332. C₂²×C₃	C₂×#64423	semidirect
338. C₂³	C₃×#64423	semidirect
342. C₇	C₂×C₃×(C₂²⋊D₇)⋊C₃	semidirect
343. C₇	C₂×C₃×D₄×ΓL(1,𝔽₈)	semidirect
354. C₂×C₃	#11924207	direct (N × H)
360. C₂²	C₂×C₃×#64423	semidirect
364. C₃	C₂×#11924207	direct (N × H)
367. C₂	C₃×#11924207	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
C₂²×C₃×#64423	2
C₂×C₃×C₇×C₂²⋊D₇	3
C₂³×C₃×#3861	2
C₃×#11924207	2
C₂×#11924207	3
C₂×C₃×D₄×ΓL(1,𝔽₈)	7
C₂×C₃×(C₂²⋊D₇)⋊C₃	7

Subgroups — C2×C3×#11924207 #72246499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#11924207 #72246499