Subgroups — #90277⋊C₃ #13057320

Order 1344.

660 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×ΓL(1,𝔽₈)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#1159⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	#10620789	C₂	1	1	yes	maximal, characteristic, complemented
5	#6502⋊C₃	C₂	1	2	yes	maximal, complemented
6	#6498⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×ΓL(1,𝔽₈)⋊C₄	C₂	1	2	yes	maximal, complemented
8	#6449⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	1	2	yes	maximal, complemented
10	#6441⋊C₃	C₂	1	2	yes	maximal, complemented
11	#6440⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#90277	C₃	1	1	yes	maximal, characteristic, complemented, Hall
13	C₂⁴×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
14	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
15	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
16	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	—
17	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic
18	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×ΓL(1,𝔽₈)⋊C₄	—	2	4	no	—
20	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
21	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
22	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	#1159⋊C₃	—	2	4	no	—
26	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
27	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
29	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
30	(C₂²⋊Dic₇)⋊C₃	C₂²	1	1	yes	characteristic
31	(C₂²⋊Dic₇)⋊C₃	C₂²	1	2	yes	—
32	(C₂²⋊Dic₇)⋊C₃	C₂²	1	2	yes	complemented
33	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	complemented
34	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	2	yes	complemented
35	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	complemented
36	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	complemented
37	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	complemented
38	C₂³×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#1159	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×#120	C₂×C₃	1	1	yes	characteristic, complemented
41	#6516	C₂×C₃	1	1	yes	characteristic, complemented
42	#6502	C₂×C₃	1	2	yes	complemented
43	#6498	C₂×C₃	1	1	yes	characteristic, complemented
44	D₄×Dic₇	C₂×C₃	1	2	yes	complemented
45	#6449	C₂×C₃	1	1	yes	characteristic, complemented
46	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
47	#6441	C₂×C₃	1	2	yes	complemented
48	#6440	C₂×C₃	1	1	yes	characteristic, complemented
49	C₃×#525	—	7	1	no	maximal, Hall
50	C₂³×ΓL(1,𝔽₈)	—	2	2	no	—
51	C₂³×ΓL(1,𝔽₈)	—	2	4	no	—
52	C₂³×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
53	C₂³×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
54	C₂³×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
55	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
56	D₄×ΓL(1,𝔽₈)	—	2	2	no	—
57	D₄×ΓL(1,𝔽₈)	—	2	4	no	—
58	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
59	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
60	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
61	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
62	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
63	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
64	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
65	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	4	no	—
66	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	4	no	—
67	C₂×ΓL(1,𝔽₈)⋊C₄	D₄	1	4	yes	complemented
68	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
70	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
71	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
73	C₄×AGL(1,𝔽₇)	—	2	2	no	—
74	ΓL(1,𝔽₈)⋊Q₈	—	2	2	no	—
75	C₂⁴×C₇	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₇×D₄	C₂²×C₃	1	2	yes	—
77	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
79	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic, complemented
81	C₂²×Dic₇	—	2	4	no	—
82	C₂²×Dic₇	C₂²×C₃	1	2	yes	—
83	C₂²×Dic₇	C₂²×C₃	1	2	yes	—
84	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
85	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
86	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
87	#1159	—	2	4	no	—
88	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
93	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	—
94	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
95	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
96	C₄⋊Dic₇	C₂²×C₃	1	2	yes	complemented
97	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
98	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
99	C₄×Dic₇	C₂²×C₃	1	2	yes	complemented
100	C₂×C₃×#41	—	7	1	no	—
101	C₂³×C₃×C₄	—	7	1	no	—
102	C₃×#123	—	7	1	no	—
103	C₃×#123	—	7	1	no	—
104	C₃×C₂²⋊Q₈	—	7	2	no	—
105	C₃×#121	—	7	2	no	—
106	C₃×#120	—	7	1	no	—
107	C₃×#120	—	7	1	no	—
108	C₃×C₄×D₄	—	7	2	no	—
109	C₃×C₄×D₄	—	7	2	no	—
110	C₃×#117	—	7	1	no	—
111	C₂²×ΓL(1,𝔽₈)	—	2	8	no	—
112	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
113	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
114	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
115	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
116	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
117	C₂²×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	—
118	C₂²×ΓL(1,𝔽₈)	#41	1	4	yes	complemented
119	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
120	C₂×AGL(1,𝔽₇)	—	2	1	no	—
121	C₂×AGL(1,𝔽₇)	—	2	2	no	—
122	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
123	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
124	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
125	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
126	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
127	ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	2	yes	—
128	ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	2	yes	—
129	#525	—	7	1	no	Sylow
130	C₂³×C₇	—	2	2	no	—
131	C₂³×C₇	—	2	4	no	—
132	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
133	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
134	C₂³×C₇	C₂³×C₃	1	2	yes	—
135	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
136	C₇×D₄	—	2	2	no	—
137	C₇×D₄	—	2	4	no	—
138	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
139	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
140	C₂²⋊D₇	—	2	2	no	—
141	C₂²⋊D₇	—	2	4	no	—
142	C₂²⋊D₇	—	2	2	no	—
143	C₂×Dic₇	—	2	2	no	—
144	C₂×Dic₇	—	2	2	no	—
145	C₂×Dic₇	—	2	4	no	—
146	C₂×Dic₇	—	2	4	no	—
147	C₂×Dic₇	C₃×D₄	1	4	yes	complemented
148	C₂×Dic₇	C₂³×C₃	1	2	yes	—
149	C₂×Dic₇	C₂³×C₃	1	2	yes	—
150	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
151	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
152	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
153	C₄×D₇	—	2	2	no	—
154	Dic₁₄	—	2	2	no	—
155	C₂⁴×C₃	—	7	1	no	—
156	C₃×#41	—	14	4	no	—
157	C₂×C₃×Q₈	—	7	1	no	—
158	C₂×C₃×D₄	—	7	2	no	—
159	C₂×C₃×D₄	—	7	1	no	—
160	C₂×C₃×D₄	—	7	1	no	—
161	C₂×C₃×D₄	—	7	2	no	—
162	C₂×C₃×D₄	—	7	1	no	—
163	C₂²×C₃×C₄	—	7	1	no	—
164	C₂²×C₃×C₄	—	7	1	no	—
165	C₂²×C₃×C₄	—	7	2	no	—
166	C₂²×C₃×C₄	—	7	2	no	—
167	C₂²×C₃×C₄	—	7	1	no	—
168	C₂²×C₃×C₄	—	7	1	no	—
169	C₂²×C₃×C₄	—	14	4	no	—
170	C₃×C₄⋊C₄	—	7	2	no	—
171	C₃×C₄⋊C₄	—	7	2	no	—
172	C₃×C₄⋊C₄	—	7	2	no	—
173	C₃×C₂²⋊C₄	—	7	1	no	—
174	C₃×C₂²⋊C₄	—	7	2	no	—
175	C₃×C₂²⋊C₄	—	7	2	no	—
176	C₃×C₂²⋊C₄	—	7	2	no	—
177	C₃×C₂²⋊C₄	—	7	1	no	—
178	C₃×C₂²⋊C₄	—	7	2	no	—
179	C₃×C₄²	—	7	2	no	—
180	C₂×ΓL(1,𝔽₈)	—	2	2	no	—
181	C₂×ΓL(1,𝔽₈)	—	2	4	no	—
182	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
183	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
184	C₂×ΓL(1,𝔽₈)	C₂×#41	1	2	yes	—
185	AGL(1,𝔽₇)	—	4	1	no	—
186	C₂×#41	—	7	1	no	—
187	C₂³×C₄	—	7	1	no	—
188	#123	—	7	1	no	—
189	#123	—	7	1	no	—
190	C₂²⋊Q₈	—	7	2	no	—
191	#121	—	7	2	no	—
192	#120	—	7	1	no	—
193	#120	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
194	C₄×D₄	—	7	2	no	—
195	C₄×D₄	—	7	2	no	—
196	#117	—	7	1	no	—
197	C₂²×C₇	—	2	8	no	—
198	C₂²×C₇	—	2	2	no	—
199	C₂²×C₇	—	2	2	no	—
200	C₂²×C₇	—	2	2	no	—
201	C₂²×C₇	—	2	1	no	—
202	C₂²×C₇	—	2	2	no	—
203	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
204	C₂²×C₇	C₃×#41	1	4	yes	complemented
205	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
206	C₂×D₇	—	2	1	no	—
207	C₂×D₇	—	2	2	no	—
208	C₄×C₇	—	2	1	no	—
209	C₄×C₇	—	2	2	no	—
210	Dic₇	—	2	1	no	—
211	Dic₇	—	2	2	no	—
212	Dic₇	—	2	2	no	—
213	Dic₇	C₂×C₃×D₄	1	2	yes	—
214	Dic₇	C₂×C₃×D₄	1	2	yes	—
215	C₂³×C₃	—	7	1	no	—
216	C₂³×C₃	—	7	1	no	—
217	C₂³×C₃	—	7	2	no	—
218	C₂³×C₃	—	7	1	no	—
219	C₂³×C₃	—	14	2	no	—
220	C₂³×C₃	—	14	4	no	—
221	C₃×Q₈	—	14	2	no	—
222	C₃×D₄	—	14	4	no	—
223	C₃×D₄	—	14	2	no	—
224	C₃×D₄	—	14	2	no	—
225	C₃×D₄	—	14	4	no	—
226	C₃×D₄	—	14	2	no	—
227	C₂×C₃×C₄	—	7	4	no	—
228	C₂×C₃×C₄	—	7	1	no	—
229	C₂×C₃×C₄	—	7	1	no	—
230	C₂×C₃×C₄	—	7	2	no	—
231	C₂×C₃×C₄	—	7	2	no	—
232	C₂×C₃×C₄	—	7	1	no	—
233	C₂×C₃×C₄	—	7	2	no	—
234	C₂×C₃×C₄	—	7	1	no	—
235	C₂×C₃×C₄	—	14	2	no	—
236	C₂×C₃×C₄	—	14	4	no	—
237	C₂×C₃×C₄	—	14	4	no	—
238	C₂×C₃×C₄	—	14	2	no	—
239	C₂×C₃×C₄	—	14	2	no	—
240	ΓL(1,𝔽₈)	#525	1	1	yes	characteristic, complemented, Hall
241	C₂⁴	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
242	#41	—	14	4	no	—
243	C₂×Q₈	—	7	1	no	—
244	C₂×D₄	—	7	2	no	—
245	C₂×D₄	—	7	1	no	—
246	C₂×D₄	—	7	1	no	—
247	C₂×D₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
248	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
249	C₂²×C₄	—	7	1	no	—
250	C₂²×C₄	—	7	2	no	—
251	C₂²×C₄	—	7	1	no	—
252	C₂²×C₄	—	7	2	no	—
253	C₂²×C₄	—	7	1	no	—
254	C₂²×C₄	—	7	1	no	—
255	C₂²×C₄	—	14	4	no	—
256	C₄⋊C₄	—	7	2	no	—
257	C₄⋊C₄	—	7	2	no	—
258	C₄⋊C₄	—	7	2	no	—
259	C₂²⋊C₄	—	7	1	no	—
260	C₂²⋊C₄	—	7	2	no	—
261	C₂²⋊C₄	—	7	2	no	—
262	C₂²⋊C₄	—	7	2	no	—
263	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
264	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
265	C₄²	—	7	2	no	—
266	C₂×C₇	—	2	2	no	—
267	C₂×C₇	—	2	4	no	—
268	C₂×C₇	—	4	1	no	—
269	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
270	C₂×C₇	C₂×C₃×#41	1	2	yes	—
271	D₇	—	4	1	no	—
272	C₂²×C₃	—	7	2	no	—
273	C₂²×C₃	—	7	4	no	—
274	C₂²×C₃	—	7	1	no	—
275	C₂²×C₃	—	14	2	no	—
276	C₂²×C₃	—	14	2	no	—
277	C₂²×C₃	—	14	2	no	—
278	C₂²×C₃	—	14	1	no	—
279	C₂²×C₃	—	14	2	no	—
280	C₂²×C₃	—	14	8	no	—
281	C₂²×C₃	—	14	1	no	—
282	C₂²×C₃	—	14	2	no	—
283	C₃×C₄	—	7	2	no	—
284	C₃×C₄	—	7	2	no	—
285	C₃×C₄	—	14	1	no	—
286	C₃×C₄	—	14	2	no	—
287	C₃×C₄	—	14	2	no	—
288	C₃×C₄	—	14	1	no	—
289	C₃×C₄	—	14	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	4	no	—
292	C₂³	—	7	1	no	—
293	C₂³	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
294	C₂³	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
295	C₂³	C₂²×AGL(1,𝔽₇)	1	2	yes	—
296	Q₈	—	14	2	no	—
297	D₄	—	2	2	no	—
298	D₄	—	2	4	no	—
299	D₄	—	14	2	no	—
300	D₄	—	14	2	no	—
301	D₄	—	14	4	no	—
302	C₂×C₄	—	7	4	no	—
303	C₂×C₄	—	7	1	no	—
304	C₂×C₄	—	7	1	no	—
305	C₂×C₄	—	7	2	no	—
306	C₂×C₄	—	7	2	no	—
307	C₂×C₄	—	7	1	no	—
308	C₂×C₄	—	14	2	no	—
309	C₂×C₄	—	14	4	no	—
310	C₂×C₄	—	14	4	no	—
311	C₂×C₄	—	14	2	no	—
312	C₂×C₄	—	14	2	no	—
313	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
314	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
315	C₇	C₃×#525	1	1	yes	characteristic, complemented, Sylow
316	C₂×C₃	—	7	1	no	—
317	C₂×C₃	—	7	2	no	—
318	C₂×C₃	—	14	2	no	—
319	C₂×C₃	—	14	4	no	—
320	C₂×C₃	—	28	1	no	—
321	C₂×C₃	—	28	1	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	14	1	no	—
329	C₂²	—	14	2	no	—
330	C₂²	D₄×AGL(1,𝔽₇)	1	2	yes	—
331	C₂²	#1159⋊C₃	1	4	yes	complemented
332	C₂²	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
333	C₄	—	2	1	no	—
334	C₄	—	2	2	no	—
335	C₄	—	7	2	no	—
336	C₄	—	7	2	no	—
337	C₄	—	14	2	no	—
338	C₄	—	14	1	no	—
339	C₄	—	14	2	no	—
340	C₃	—	7	1	no	Sylow
341	C₂	—	2	2	no	—
342	C₂	—	2	4	no	—
343	C₂	—	4	1	no	—
344	C₂	—	28	1	no	—
345	C₂	C₂×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
346	C₂	C₂×#1159⋊C₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₇	C₂⁴×C₃
Fitting	C₇×#120	C₂×C₃
hypercenter	#120	AGL(1,𝔽₇)
hypocenter	C₇	C₃×#525
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #120

Complements

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

N	H ≅ G/N	type
1. C₂³×ΓL(1,𝔽₈)⋊C₄	C₂	semidirect
2. C₂×#1159⋊C₃	C₂	semidirect
3. ΓL(1,𝔽₈)×#120	C₂	semidirect
4. #10620789	C₂	semidirect
5. #6502⋊C₃	C₂	semidirect
6. #6498⋊C₃	C₂	semidirect
7. D₄×ΓL(1,𝔽₈)⋊C₄	C₂	semidirect
8. #6449⋊C₃	C₂	semidirect
9. ((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	semidirect
10. #6441⋊C₃	C₂	semidirect
11. #6440⋊C₃	C₂	semidirect
12. #90277	C₃	semidirect
18. C₂×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
24. C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
26. C₂×C₄×AGL(1,𝔽₇)	C₂²	semidirect
27. C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	semidirect
32. (C₂²⋊Dic₇)⋊C₃	C₂²	semidirect
33. (C₂×AGL(1,𝔽₇))⋊C₄	C₂²	semidirect
34. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	semidirect
35. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	semidirect
36. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	semidirect
37. C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
38. C₂³×Dic₇	C₂×C₃	semidirect
39. C₂×#1159	C₂×C₃	semidirect
40. C₇×#120	C₂×C₃	semidirect
41. #6516	C₂×C₃	semidirect
42. #6502	C₂×C₃	semidirect
43. #6498	C₂×C₃	semidirect
44. D₄×Dic₇	C₂×C₃	semidirect
45. #6449	C₂×C₃	semidirect
46. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
47. #6441	C₂×C₃	semidirect
48. #6440	C₂×C₃	semidirect
67. C₂×ΓL(1,𝔽₈)⋊C₄	D₄	semidirect
80. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
86. C₂²×Dic₇	C₂²×C₃	semidirect
88. C₂×C₄×D₇	C₂²×C₃	semidirect
89. C₂×Dic₁₄	C₂²×C₃	semidirect
94. C₂²⋊Dic₇	C₂²×C₃	semidirect
95. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
96. C₄⋊Dic₇	C₂²×C₃	semidirect
97. Dic₇⋊C₄	C₂²×C₃	semidirect
98. Dic₇⋊C₄	C₂²×C₃	semidirect
99. C₄×Dic₇	C₂²×C₃	semidirect
118. C₂²×ΓL(1,𝔽₈)	#41	semidirect
147. C₂×Dic₇	C₃×D₄	semidirect
193. #120	AGL(1,𝔽₇)	semidirect
204. C₂²×C₇	C₃×#41	semidirect
240. ΓL(1,𝔽₈)	#525	semidirect
315. C₇	C₃×#525	semidirect
331. C₂²	#1159⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×ΓL(1,𝔽₈)⋊C₄	2
C₂×#1159⋊C₃	2
ΓL(1,𝔽₈)×#120	2
#10620789	2
#6502⋊C₃	2
#6498⋊C₃	2
D₄×ΓL(1,𝔽₈)⋊C₄	2
#6449⋊C₃	2
((C₂²⋊D₇)⋊C₃)⋊C₄	2
#6441⋊C₃	2
#6440⋊C₃	2
#90277	3
C₃×#525	7

Subgroups — #90277⋊C3 #13057320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #90277⋊C₃ #13057320