Subgroups — C₂²×#6548⋊C₃ #72277377

Order 2688.

13120 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×(C₂²⋊D₇)⋊C₃	C₂	1	4	yes	maximal, complemented
3	C₂×#6548⋊C₃	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#1159⋊C₃	C₂	1	4	yes	maximal, complemented
5	C₂²×D₄×AGL(1,𝔽₇)	C₂	1	4	yes	maximal, complemented
6	C₂²×#1157⋊C₃	C₂	1	2	yes	maximal, complemented
7	C₂²×#6548	C₃	1	1	yes	maximal, characteristic, complemented, Hall
8	C₂⁵×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
9	C₂⁴×AGL(1,𝔽₇)	C₂²	1	4	yes	complemented
10	C₂²×D₄×ΓL(1,𝔽₈)	C₂²	1	4	yes	complemented
11	C₂²×D₄×ΓL(1,𝔽₈)	C₂²	1	24	yes	complemented
12	C₂³×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
13	C₂²×(C₂²⋊D₇)⋊C₃	C₂²	1	4	yes	complemented
14	C₂²×(C₂²⋊D₇)⋊C₃	C₂²	1	8	yes	complemented
15	C₂²×(C₂²⋊D₇)⋊C₃	C₂²	1	96	yes	complemented
16	C₂³×ΓL(1,𝔽₈)⋊C₄	C₂²	1	4	yes	complemented
17	#6548⋊C₃	C₂²	1	256	yes	direct product factor
18	C₂×#1159⋊C₃	C₂²	1	96	yes	complemented
19	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	96	yes	complemented
20	C₂×#1157⋊C₃	C₂²	1	48	yes	complemented
21	C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
22	C₂²×C₄×AGL(1,𝔽₇)	C₂²	1	4	yes	complemented
23	C₂²×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	2	yes	complemented
24	C₂³×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂³×C₂²⋊D₇	C₂×C₃	1	4	yes	complemented
26	C₂×#6548	C₂×C₃	1	48	yes	complemented
27	C₂²×#1159	C₂×C₃	1	4	yes	complemented
28	C₂²×D₄×D₇	C₂×C₃	1	4	yes	complemented
29	C₂²×#1157	C₂×C₃	1	2	yes	complemented
30	C₂²×C₃×H(5,𝔽₂)	—	7	1	no	maximal, Hall
31	C₂⁴×ΓL(1,𝔽₈)	—	4	8	no	—
32	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	4	yes	—
33	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
34	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	24	yes	complemented
35	C₂³×AGL(1,𝔽₇)	—	4	16	no	—
36	C₂³×AGL(1,𝔽₇)	C₂³	1	4	yes	—
37	C₂³×AGL(1,𝔽₇)	C₂³	1	48	yes	complemented
38	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	48	yes	complemented
39	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	64	yes	complemented
40	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
41	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	12	yes	complemented
42	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	48	yes	complemented
43	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	96	yes	complemented
44	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	256	yes	complemented
45	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	1	4	yes	—
46	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	1	48	yes	complemented
47	#1159⋊C₃	C₂³	1	256	yes	complemented
48	D₄×AGL(1,𝔽₇)	C₂³	1	256	yes	complemented
49	#1157⋊C₃	C₂³	1	128	yes	complemented
50	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	24	yes	complemented
51	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	48	yes	complemented
52	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂³	1	24	yes	complemented
53	C₂⁵×C₇	C₂²×C₃	1	2	yes	complemented
54	C₂⁴×D₇	C₂²×C₃	1	4	yes	complemented
55	C₂²×C₇×D₄	C₂²×C₃	1	4	yes	complemented
56	C₂²×C₇×D₄	C₂²×C₃	1	24	yes	complemented
57	C₂³×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
58	C₂²×C₂²⋊D₇	C₂²×C₃	1	4	yes	complemented
59	C₂²×C₂²⋊D₇	C₂²×C₃	1	8	yes	complemented
60	C₂²×C₂²⋊D₇	C₂²×C₃	1	96	yes	complemented
61	C₂³×Dic₇	C₂²×C₃	1	4	yes	complemented
62	#6548	C₂²×C₃	1	256	yes	complemented
63	C₂×#1159	C₂²×C₃	1	96	yes	complemented
64	C₂×D₄×D₇	C₂²×C₃	1	96	yes	complemented
65	C₂×#1157	C₂²×C₃	1	48	yes	complemented
66	C₂²×D₂₈	C₂²×C₃	1	2	yes	complemented
67	C₂²×C₄×D₇	C₂²×C₃	1	4	yes	complemented
68	C₂²×Dic₁₄	C₂²×C₃	1	2	yes	complemented
69	C₂×C₃×H(5,𝔽₂)	—	7	48	no	—
70	C₂²×C₃×#41	—	7	2	no	—
71	C₂²×C₃×#41	—	7	4	no	—
72	C₂³×C₃×D₄	—	7	4	no	—
73	C₂³×C₃×D₄	—	7	4	no	—
74	C₂³×C₃×D₄	—	7	1	no	—
75	C₂³×ΓL(1,𝔽₈)	—	2	16	no	—
76	C₂³×ΓL(1,𝔽₈)	—	2	4	no	—
77	C₂³×ΓL(1,𝔽₈)	—	4	48	no	—
78	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	24	yes	—
79	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	6	yes	—
80	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
81	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	32	yes	complemented
82	C₂²×AGL(1,𝔽₇)	—	2	16	no	—
83	C₂²×AGL(1,𝔽₇)	—	4	96	no	—
84	C₂²×AGL(1,𝔽₇)	C₂⁴	1	24	yes	—
85	C₂²×AGL(1,𝔽₇)	C₂⁴	1	64	yes	complemented
86	D₄×ΓL(1,𝔽₈)	C₂⁴	1	64	yes	complemented
87	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	12	yes	—
88	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	16	yes	complemented
89	(C₂²⋊D₇)⋊C₃	C₂⁴	1	64	yes	complemented
90	(C₂²⋊D₇)⋊C₃	C₂⁴	1	128	yes	complemented
91	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	24	yes	—
92	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	64	yes	complemented
93	C₄⋊AGL(1,𝔽₇)	C₂⁴	1	32	yes	complemented
94	C₄×AGL(1,𝔽₇)	C₂⁴	1	64	yes	complemented
95	ΓL(1,𝔽₈)⋊Q₈	C₂⁴	1	32	yes	complemented
96	C₂²×H(5,𝔽₂)	—	7	1	no	Sylow
97	C₂⁴×C₇	—	4	8	no	—
98	C₂⁴×C₇	C₂³×C₃	1	4	yes	—
99	C₂⁴×C₇	C₂³×C₃	1	1	yes	characteristic
100	C₂⁴×C₇	C₂³×C₃	1	24	yes	complemented
101	C₂³×D₇	—	4	16	no	—
102	C₂³×D₇	C₂³×C₃	1	4	yes	—
103	C₂³×D₇	C₂³×C₃	1	48	yes	complemented
104	C₂×C₇×D₄	C₂³×C₃	1	48	yes	complemented
105	C₂×C₇×D₄	C₂³×C₃	1	64	yes	complemented
106	C₂²×C₄×C₇	C₂³×C₃	1	2	yes	—
107	C₂²×C₄×C₇	C₂³×C₃	1	12	yes	complemented
108	C₂×C₂²⋊D₇	C₂³×C₃	1	48	yes	complemented
109	C₂×C₂²⋊D₇	C₂³×C₃	1	96	yes	complemented
110	C₂×C₂²⋊D₇	C₂³×C₃	1	256	yes	complemented
111	C₂²×Dic₇	C₂³×C₃	1	4	yes	—
112	C₂²×Dic₇	C₂³×C₃	1	48	yes	complemented
113	#1159	C₂³×C₃	1	256	yes	complemented
114	D₄×D₇	C₂³×C₃	1	256	yes	complemented
115	#1157	C₂³×C₃	1	128	yes	complemented
116	C₂×D₂₈	C₂³×C₃	1	24	yes	complemented
117	C₂×C₄×D₇	C₂³×C₃	1	48	yes	complemented
118	C₂×Dic₁₄	C₂³×C₃	1	24	yes	complemented
119	C₂⁵×C₃	—	7	4	no	—
120	C₂⁵×C₃	—	7	2	no	—
121	C₃×H(5,𝔽₂)	—	7	256	no	—
122	C₂×C₃×#41	—	7	48	no	—
123	C₂×C₃×#41	—	7	96	no	—
124	C₂²×C₃×Q₈	—	7	2	no	—
125	C₂²×C₃×D₄	—	7	2	no	—
126	C₂²×C₃×D₄	—	7	96	no	—
127	C₂²×C₃×D₄	—	7	4	no	—
128	C₂²×C₃×D₄	—	7	8	no	—
129	C₂²×C₃×D₄	—	7	96	no	—
130	C₂²×C₃×D₄	—	7	4	no	—
131	C₂²×C₃×D₄	—	7	24	no	—
132	C₂³×C₃×C₄	—	7	4	no	—
133	C₂³×C₃×C₄	—	7	4	no	—
134	C₂³×C₃×C₄	—	7	1	no	—
135	C₂²×ΓL(1,𝔽₈)	—	2	48	no	—
136	C₂²×ΓL(1,𝔽₈)	—	2	12	no	—
137	C₂²×ΓL(1,𝔽₈)	—	4	32	no	—
138	C₂²×ΓL(1,𝔽₈)	H(5,𝔽₂)	1	4	yes	complemented
139	C₂²×ΓL(1,𝔽₈)	C₂⁵	1	16	yes	—
140	C₂²×ΓL(1,𝔽₈)	C₂⁵	1	4	yes	—
141	C₂²×ΓL(1,𝔽₈)	C₂⁵	1	3	yes	—
142	C₂×AGL(1,𝔽₇)	—	2	48	no	—
143	C₂×AGL(1,𝔽₇)	—	4	64	no	—
144	C₂×AGL(1,𝔽₇)	C₂⁵	1	16	yes	—
145	C₄×ΓL(1,𝔽₈)	C₂⁵	1	8	yes	—
146	ΓL(1,𝔽₈)⋊C₄	C₂⁵	1	16	yes	—
147	C₂×H(5,𝔽₂)	—	7	48	no	—
148	C₂²×#41	—	7	4	no	—
149	C₂²×#41	—	7	2	no	—
150	C₂³×D₄	—	7	4	no	—
151	C₂³×D₄	—	7	4	no	—
152	C₂³×D₄	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
153	C₂³×C₇	—	2	16	no	—
154	C₂³×C₇	—	2	4	no	—
155	C₂³×C₇	—	4	48	no	—
156	C₂³×C₇	C₂⁴×C₃	1	24	yes	—
157	C₂³×C₇	C₂⁴×C₃	1	6	yes	—
158	C₂³×C₇	C₂⁴×C₃	1	1	yes	characteristic
159	C₂³×C₇	C₂⁴×C₃	1	32	yes	complemented
160	C₂²×D₇	—	2	16	no	—
161	C₂²×D₇	—	4	96	no	—
162	C₂²×D₇	C₂⁴×C₃	1	24	yes	—
163	C₂²×D₇	C₂⁴×C₃	1	64	yes	complemented
164	C₇×D₄	C₂⁴×C₃	1	64	yes	complemented
165	C₂×C₄×C₇	C₂⁴×C₃	1	12	yes	—
166	C₂×C₄×C₇	C₂⁴×C₃	1	16	yes	complemented
167	C₂²⋊D₇	C₂⁴×C₃	1	64	yes	complemented
168	C₂²⋊D₇	C₂⁴×C₃	1	128	yes	complemented
169	C₂×Dic₇	C₂⁴×C₃	1	24	yes	—
170	C₂×Dic₇	C₂⁴×C₃	1	64	yes	complemented
171	D₂₈	C₂⁴×C₃	1	32	yes	complemented
172	C₄×D₇	C₂⁴×C₃	1	64	yes	complemented
173	Dic₁₄	C₂⁴×C₃	1	32	yes	complemented
174	C₂⁴×C₃	—	7	4	no	—
175	C₂⁴×C₃	—	7	48	no	—
176	C₂⁴×C₃	—	7	4	no	—
177	C₂⁴×C₃	—	7	1	no	—
178	C₂⁴×C₃	—	7	24	no	—
179	C₂⁴×C₃	—	28	8	no	—
180	C₂⁴×C₃	—	28	16	no	—
181	C₃×#41	—	7	128	no	—
182	C₃×#41	—	7	256	no	—
183	C₂×C₃×Q₈	—	7	24	no	—
184	C₂×C₃×D₄	—	7	24	no	—
185	C₂×C₃×D₄	—	7	256	no	—
186	C₂×C₃×D₄	—	7	48	no	—
187	C₂×C₃×D₄	—	7	96	no	—
188	C₂×C₃×D₄	—	7	256	no	—
189	C₂×C₃×D₄	—	7	48	no	—
190	C₂×C₃×D₄	—	7	64	no	—
191	C₂²×C₃×C₄	—	7	48	no	—
192	C₂²×C₃×C₄	—	7	4	no	—
193	C₂²×C₃×C₄	—	7	48	no	—
194	C₂²×C₃×C₄	—	7	2	no	—
195	C₂²×C₃×C₄	—	7	12	no	—
196	C₂×ΓL(1,𝔽₈)	—	2	16	no	—
197	C₂×ΓL(1,𝔽₈)	—	2	4	no	—
198	C₂×ΓL(1,𝔽₈)	C₂×H(5,𝔽₂)	1	6	yes	complemented
199	C₂×ΓL(1,𝔽₈)	C₂⁶	1	1	yes	characteristic
200	AGL(1,𝔽₇)	—	2	16	no	—
201	C₂⁵	—	7	4	no	—
202	C₂⁵	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
203	H(5,𝔽₂)	—	7	256	no	—
204	C₂×#41	—	7	96	no	—
205	C₂×#41	—	7	48	no	—
206	C₂²×Q₈	—	7	2	no	—
207	C₂²×D₄	—	7	8	no	—
208	C₂²×D₄	—	7	4	no	—
209	C₂²×D₄	—	7	96	no	—
210	C₂²×D₄	—	7	96	no	—
211	C₂²×D₄	—	7	2	no	—
212	C₂²×D₄	C₂×AGL(1,𝔽₇)	1	4	yes	complemented
213	C₂²×D₄	C₂×AGL(1,𝔽₇)	1	24	yes	complemented
214	C₂³×C₄	—	7	4	no	—
215	C₂³×C₄	—	7	4	no	—
216	C₂³×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
217	C₂²×C₇	—	2	48	no	—
218	C₂²×C₇	—	2	12	no	—
219	C₂²×C₇	—	4	32	no	—
220	C₂²×C₇	C₃×H(5,𝔽₂)	1	4	yes	complemented
221	C₂²×C₇	C₂⁵×C₃	1	16	yes	—
222	C₂²×C₇	C₂⁵×C₃	1	4	yes	—
223	C₂²×C₇	C₂⁵×C₃	1	3	yes	—
224	C₂×D₇	—	2	48	no	—
225	C₂×D₇	—	4	64	no	—
226	C₂×D₇	C₂⁵×C₃	1	16	yes	—
227	C₄×C₇	C₂⁵×C₃	1	8	yes	—
228	Dic₇	C₂⁵×C₃	1	16	yes	—
229	C₂³×C₃	—	7	24	no	—
230	C₂³×C₃	—	7	64	no	—
231	C₂³×C₃	—	7	24	no	—
232	C₂³×C₃	—	7	6	no	—
233	C₂³×C₃	—	7	1	no	—
234	C₂³×C₃	—	7	32	no	—
235	C₂³×C₃	—	14	4	no	—
236	C₂³×C₃	—	14	16	no	—
237	C₂³×C₃	—	14	16	no	—
238	C₂³×C₃	—	28	48	no	—
239	C₂³×C₃	—	28	96	no	—
240	C₃×Q₈	—	7	32	no	—
241	C₃×D₄	—	7	32	no	—
242	C₃×D₄	—	7	64	no	—
243	C₃×D₄	—	7	128	no	—
244	C₃×D₄	—	7	64	no	—
245	C₂×C₃×C₄	—	7	64	no	—
246	C₂×C₃×C₄	—	7	24	no	—
247	C₂×C₃×C₄	—	7	64	no	—
248	C₂×C₃×C₄	—	7	12	no	—
249	C₂×C₃×C₄	—	7	16	no	—
250	ΓL(1,𝔽₈)	C₂²×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
251	C₂⁴	—	4	8	no	—
252	C₂⁴	—	7	4	no	—
253	C₂⁴	—	7	48	no	—
254	C₂⁴	—	28	16	no	—
255	C₂⁴	C₂²×AGL(1,𝔽₇)	1	4	yes	—
256	C₂⁴	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
257	C₂⁴	C₂²×AGL(1,𝔽₇)	1	24	yes	complemented
258	#41	—	7	256	no	—
259	#41	—	7	128	no	—
260	C₂×Q₈	—	7	24	no	—
261	C₂×D₄	—	7	96	no	—
262	C₂×D₄	—	7	48	no	—
263	C₂×D₄	—	7	256	no	—
264	C₂×D₄	—	7	256	no	—
265	C₂×D₄	—	7	24	no	—
266	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	48	yes	complemented
267	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	64	yes	complemented
268	C₂²×C₄	—	7	48	no	—
269	C₂²×C₄	—	7	4	no	—
270	C₂²×C₄	—	7	48	no	—
271	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
272	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	12	yes	complemented
273	C₂×C₇	—	2	16	no	—
274	C₂×C₇	—	2	4	no	—
275	C₂×C₇	C₂×C₃×H(5,𝔽₂)	1	6	yes	complemented
276	C₂×C₇	C₂⁶×C₃	1	1	yes	characteristic
277	D₇	—	2	16	no	—
278	C₂²×C₃	—	7	16	no	—
279	C₂²×C₃	—	7	4	no	—
280	C₂²×C₃	—	7	3	no	—
281	C₂²×C₃	—	7	16	no	—
282	C₂²×C₃	—	7	4	no	—
283	C₂²×C₃	—	14	12	no	—
284	C₂²×C₃	—	14	48	no	—
285	C₂²×C₃	—	14	48	no	—
286	C₂²×C₃	—	28	32	no	—
287	C₂²×C₃	—	28	64	no	—
288	C₃×C₄	—	7	16	no	—
289	C₃×C₄	—	7	8	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	2	16	no	—
292	C₂³	—	4	48	no	—
293	C₂³	—	7	24	no	—
294	C₂³	—	7	64	no	—
295	C₂³	—	14	16	no	—
296	C₂³	—	28	96	no	—
297	C₂³	C₂³×AGL(1,𝔽₇)	1	24	yes	—
298	C₂³	C₂³×AGL(1,𝔽₇)	1	6	yes	—
299	C₂³	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
300	C₂³	C₂³×AGL(1,𝔽₇)	1	32	yes	complemented
301	Q₈	—	7	32	no	—
302	D₄	—	7	128	no	—
303	D₄	—	7	64	no	—
304	D₄	—	7	32	no	—
305	D₄	C₂³×AGL(1,𝔽₇)	1	64	yes	complemented
306	C₂×C₄	—	7	24	no	—
307	C₂×C₄	—	7	64	no	—
308	C₂×C₄	—	7	64	no	—
309	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	12	yes	—
310	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	16	yes	complemented
311	C₇	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
312	C₂×C₃	—	7	6	no	—
313	C₂×C₃	—	7	1	no	—
314	C₂×C₃	—	14	4	no	—
315	C₂×C₃	—	14	16	no	—
316	C₂×C₃	—	14	16	no	—
317	C₂²	—	2	12	no	—
318	C₂²	—	2	48	no	—
319	C₂²	—	4	32	no	—
320	C₂²	—	7	16	no	—
321	C₂²	—	14	48	no	—
322	C₂²	—	28	64	no	—
323	C₂²	#6548⋊C₃	1	4	yes	direct product factor
324	C₂²	C₂⁴×AGL(1,𝔽₇)	1	16	yes	—
325	C₂²	C₂⁴×AGL(1,𝔽₇)	1	4	yes	—
326	C₂²	C₂⁴×AGL(1,𝔽₇)	1	3	yes	—
327	C₄	—	7	16	no	—
328	C₄	C₂⁴×AGL(1,𝔽₇)	1	8	yes	—
329	C₃	—	7	1	no	Sylow
330	C₂	—	2	4	no	—
331	C₂	—	2	16	no	—
332	C₂	—	14	16	no	—
333	C₂	C₂×#6548⋊C₃	1	6	yes	direct product factor
334	C₂	C₂⁵×AGL(1,𝔽₇)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×AGL(1,𝔽₇)
commutator, cosocle	C₂×C₇	C₂⁶×C₃
Frattini	C₂	C₂⁵×AGL(1,𝔽₇)
Fitting	C₂³×C₇×D₄	C₂×C₃
socle	C₂³×C₇	C₂⁴×C₃
hypercenter	C₂³×D₄	AGL(1,𝔽₇)
hypocenter	C₇	C₂²×C₃×H(5,𝔽₂)
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×ΓL(1,𝔽₈)	C₂	semidirect
2. C₂³×(C₂²⋊D₇)⋊C₃	C₂	semidirect
3. C₂×#6548⋊C₃	C₂	direct (N × H)
4. C₂²×#1159⋊C₃	C₂	semidirect
5. C₂²×D₄×AGL(1,𝔽₇)	C₂	semidirect
6. C₂²×#1157⋊C₃	C₂	semidirect
7. C₂²×#6548	C₃	semidirect
8. C₂⁵×ΓL(1,𝔽₈)	C₂²	semidirect
9. C₂⁴×AGL(1,𝔽₇)	C₂²	semidirect
10. C₂²×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
11. C₂²×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
12. C₂³×C₄×ΓL(1,𝔽₈)	C₂²	semidirect
13. C₂²×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
14. C₂²×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
15. C₂²×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
16. C₂³×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
17. #6548⋊C₃	C₂²	direct (N × H)
18. C₂×#1159⋊C₃	C₂²	semidirect
19. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
20. C₂×#1157⋊C₃	C₂²	semidirect
21. C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
22. C₂²×C₄×AGL(1,𝔽₇)	C₂²	semidirect
23. C₂²×ΓL(1,𝔽₈)⋊Q₈	C₂²	semidirect
24. C₂³×C₇×D₄	C₂×C₃	semidirect
25. C₂³×C₂²⋊D₇	C₂×C₃	semidirect
26. C₂×#6548	C₂×C₃	semidirect
27. C₂²×#1159	C₂×C₃	semidirect
28. C₂²×D₄×D₇	C₂×C₃	semidirect
29. C₂²×#1157	C₂×C₃	semidirect
34. C₂⁴×ΓL(1,𝔽₈)	C₂³	semidirect
37. C₂³×AGL(1,𝔽₇)	C₂³	semidirect
38. C₂×D₄×ΓL(1,𝔽₈)	C₂³	semidirect
39. C₂×D₄×ΓL(1,𝔽₈)	C₂³	semidirect
41. C₂²×C₄×ΓL(1,𝔽₈)	C₂³	semidirect
42. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
43. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
44. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
46. C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
47. #1159⋊C₃	C₂³	semidirect
48. D₄×AGL(1,𝔽₇)	C₂³	semidirect
49. #1157⋊C₃	C₂³	semidirect
50. C₂×C₄⋊AGL(1,𝔽₇)	C₂³	semidirect
51. C₂×C₄×AGL(1,𝔽₇)	C₂³	semidirect
52. C₂×ΓL(1,𝔽₈)⋊Q₈	C₂³	semidirect
53. C₂⁵×C₇	C₂²×C₃	semidirect
54. C₂⁴×D₇	C₂²×C₃	semidirect
55. C₂²×C₇×D₄	C₂²×C₃	semidirect
56. C₂²×C₇×D₄	C₂²×C₃	semidirect
57. C₂³×C₄×C₇	C₂²×C₃	semidirect
58. C₂²×C₂²⋊D₇	C₂²×C₃	semidirect
59. C₂²×C₂²⋊D₇	C₂²×C₃	semidirect
60. C₂²×C₂²⋊D₇	C₂²×C₃	semidirect
61. C₂³×Dic₇	C₂²×C₃	semidirect
62. #6548	C₂²×C₃	semidirect
63. C₂×#1159	C₂²×C₃	semidirect
64. C₂×D₄×D₇	C₂²×C₃	semidirect
65. C₂×#1157	C₂²×C₃	semidirect
66. C₂²×D₂₈	C₂²×C₃	semidirect
67. C₂²×C₄×D₇	C₂²×C₃	semidirect
68. C₂²×Dic₁₄	C₂²×C₃	semidirect
81. C₂³×ΓL(1,𝔽₈)	C₂⁴	semidirect
85. C₂²×AGL(1,𝔽₇)	C₂⁴	semidirect
86. D₄×ΓL(1,𝔽₈)	C₂⁴	semidirect
88. C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	semidirect
89. (C₂²⋊D₇)⋊C₃	C₂⁴	semidirect
90. (C₂²⋊D₇)⋊C₃	C₂⁴	semidirect
92. C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	semidirect
93. C₄⋊AGL(1,𝔽₇)	C₂⁴	semidirect
94. C₄×AGL(1,𝔽₇)	C₂⁴	semidirect
95. ΓL(1,𝔽₈)⋊Q₈	C₂⁴	semidirect
100. C₂⁴×C₇	C₂³×C₃	semidirect
103. C₂³×D₇	C₂³×C₃	semidirect
104. C₂×C₇×D₄	C₂³×C₃	semidirect
105. C₂×C₇×D₄	C₂³×C₃	semidirect
107. C₂²×C₄×C₇	C₂³×C₃	semidirect
108. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
109. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
110. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
112. C₂²×Dic₇	C₂³×C₃	semidirect
113. #1159	C₂³×C₃	semidirect
114. D₄×D₇	C₂³×C₃	semidirect
115. #1157	C₂³×C₃	semidirect
116. C₂×D₂₈	C₂³×C₃	semidirect
117. C₂×C₄×D₇	C₂³×C₃	semidirect
118. C₂×Dic₁₄	C₂³×C₃	semidirect
138. C₂²×ΓL(1,𝔽₈)	H(5,𝔽₂)	semidirect
152. C₂³×D₄	AGL(1,𝔽₇)	semidirect
159. C₂³×C₇	C₂⁴×C₃	semidirect
163. C₂²×D₇	C₂⁴×C₃	semidirect
164. C₇×D₄	C₂⁴×C₃	semidirect
166. C₂×C₄×C₇	C₂⁴×C₃	semidirect
167. C₂²⋊D₇	C₂⁴×C₃	semidirect
168. C₂²⋊D₇	C₂⁴×C₃	semidirect
170. C₂×Dic₇	C₂⁴×C₃	semidirect
171. D₂₈	C₂⁴×C₃	semidirect
172. C₄×D₇	C₂⁴×C₃	semidirect
173. Dic₁₄	C₂⁴×C₃	semidirect
198. C₂×ΓL(1,𝔽₈)	C₂×H(5,𝔽₂)	semidirect
202. C₂⁵	C₂×AGL(1,𝔽₇)	semidirect
212. C₂²×D₄	C₂×AGL(1,𝔽₇)	semidirect
213. C₂²×D₄	C₂×AGL(1,𝔽₇)	semidirect
216. C₂³×C₄	C₂×AGL(1,𝔽₇)	semidirect
220. C₂²×C₇	C₃×H(5,𝔽₂)	semidirect
250. ΓL(1,𝔽₈)	C₂²×H(5,𝔽₂)	semidirect
257. C₂⁴	C₂²×AGL(1,𝔽₇)	semidirect
266. C₂×D₄	C₂²×AGL(1,𝔽₇)	semidirect
267. C₂×D₄	C₂²×AGL(1,𝔽₇)	semidirect
272. C₂²×C₄	C₂²×AGL(1,𝔽₇)	semidirect
275. C₂×C₇	C₂×C₃×H(5,𝔽₂)	semidirect
300. C₂³	C₂³×AGL(1,𝔽₇)	semidirect
305. D₄	C₂³×AGL(1,𝔽₇)	semidirect
310. C₂×C₄	C₂³×AGL(1,𝔽₇)	semidirect
311. C₇	C₂²×C₃×H(5,𝔽₂)	semidirect
323. C₂²	#6548⋊C₃	direct (N × H)
333. C₂	C₂×#6548⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×ΓL(1,𝔽₈)	2
C₂³×(C₂²⋊D₇)⋊C₃	2
C₂×#6548⋊C₃	2
C₂²×#1159⋊C₃	2
C₂²×D₄×AGL(1,𝔽₇)	2
C₂²×#1157⋊C₃	2
C₂²×#6548	3
C₂²×C₃×H(5,𝔽₂)	7

Subgroups — C22×#6548⋊C3 #72277377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#6548⋊C₃ #72277377