Subgroups — C₄×#1159⋊C₃ #13057282

Order 1344.

620 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1159⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×D₄×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×ΓL(1,𝔽₈)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×(C₂²⋊D₇)⋊C₃	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×ΓL(1,𝔽₈)⋊C₄	C₂	1	2	yes	maximal, complemented
6	#6455⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#6450⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	1	2	yes	maximal, complemented
9	#6440⋊C₃	C₂	1	2	yes	maximal, complemented
10	C₄²×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×ΓL(1,𝔽₈)⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#1159	C₃	1	1	yes	maximal, characteristic, complemented, Hall
13	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
14	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
15	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	—
16	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
17	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
18	#1159⋊C₃	C₄	1	8	yes	direct product factor
19	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
20	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
21	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
22	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	1	yes	characteristic
23	C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
24	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
25	C₄²×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
26	(C₂²⋊Dic₇)⋊C₃	C₂²	1	2	yes	—
27	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	—
28	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	1	yes	characteristic
29	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	—
30	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	—
31	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
32	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
36	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
37	C₂×#1159	C₂×C₃	1	1	yes	characteristic
38	C₄×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
39	D₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
40	C₄×C₂²⋊D₇	C₂×C₃	1	2	yes	complemented
41	C₂×C₄×Dic₇	C₂×C₃	1	2	yes	complemented
42	#6455	C₂×C₃	1	1	yes	characteristic, complemented
43	#6450	C₂×C₃	1	1	yes	characteristic, complemented
44	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
45	#6440	C₂×C₃	1	2	yes	complemented
46	C₄²×D₇	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×Dic₁₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₃×C₄×#41	—	7	1	no	maximal, Hall
49	C₂³×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
50	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
51	D₄×ΓL(1,𝔽₈)	C₂×C₄	1	4	yes	complemented
52	C₂×C₄×ΓL(1,𝔽₈)	—	2	4	no	—
53	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
54	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
55	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
56	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
57	(C₂²⋊D₇)⋊C₃	C₂×C₄	1	8	yes	complemented
58	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	4	no	—
59	C₂×ΓL(1,𝔽₈)⋊C₄	C₂×C₄	1	8	yes	complemented
60	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
62	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
63	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
65	C₄×AGL(1,𝔽₇)	—	2	2	no	—
66	C₄×AGL(1,𝔽₇)	—	2	2	no	—
67	C₄×AGL(1,𝔽₇)	C₂×C₄	1	4	yes	complemented
68	ΓL(1,𝔽₈)⋊Q₈	C₂×C₄	1	4	yes	complemented
69	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	—
71	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
72	C₂²×Dic₇	C₂²×C₃	1	2	yes	—
73	C₂²×Dic₇	C₂²×C₃	1	2	yes	—
74	#1159	C₃×C₄	1	8	yes	complemented
75	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
78	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
79	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic
82	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	—
83	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
84	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
85	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
86	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
87	C₄×Dic₇	C₂²×C₃	1	2	yes	—
88	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
89	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
90	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
91	C₄×Dic₇	C₂²×C₃	1	2	yes	—
92	C₄×Dic₇	C₂²×C₃	1	2	yes	—
93	C₂×C₃×#41	—	7	1	no	—
94	C₃×C₄×Q₈	—	7	1	no	—
95	C₃×C₄×Q₈	—	7	1	no	—
96	C₃×C₄×D₄	—	7	2	no	—
97	C₃×C₄×D₄	—	7	2	no	—
98	C₃×C₄×D₄	—	7	1	no	—
99	C₃×C₄×D₄	—	7	1	no	—
100	C₃×#117	—	7	2	no	—
101	C₃×#117	—	7	1	no	—
102	C₂×C₃×C₄²	—	7	1	no	—
103	C₂×C₃×C₄²	—	7	2	no	—
104	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
105	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
106	C₂²×ΓL(1,𝔽₈)	C₂²×C₄	1	4	yes	—
107	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
108	C₂×AGL(1,𝔽₇)	—	2	1	no	—
109	C₂×AGL(1,𝔽₇)	—	2	1	no	—
110	C₂×AGL(1,𝔽₇)	C₂²×C₄	1	2	yes	—
111	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
112	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
113	C₄×ΓL(1,𝔽₈)	C₂²×C₄	1	2	yes	—
114	C₄×ΓL(1,𝔽₈)	#41	1	2	yes	complemented
115	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
116	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
117	ΓL(1,𝔽₈)⋊C₄	C₂²×C₄	1	4	yes	—
118	ΓL(1,𝔽₈)⋊C₄	C₂²×C₄	1	2	yes	—
119	ΓL(1,𝔽₈)⋊C₄	#41	1	2	yes	complemented
120	C₄×#41	—	7	1	no	Sylow
121	C₂³×C₇	C₂³×C₃	1	2	yes	—
122	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
123	C₇×D₄	C₂×C₃×C₄	1	4	yes	complemented
124	C₂×C₄×C₇	—	2	4	no	—
125	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
126	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
127	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
128	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
129	C₂²⋊D₇	C₂×C₃×C₄	1	8	yes	complemented
130	C₂×Dic₇	—	2	4	no	—
131	C₂×Dic₇	C₂×C₃×C₄	1	8	yes	complemented
132	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
133	C₂×Dic₇	C₂³×C₃	1	2	yes	—
134	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
135	C₂×Dic₇	C₂³×C₃	1	2	yes	—
136	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
137	C₄×D₇	—	2	2	no	—
138	C₄×D₇	—	2	2	no	—
139	C₄×D₇	C₂×C₃×C₄	1	4	yes	complemented
140	Dic₁₄	C₂×C₃×C₄	1	4	yes	complemented
141	C₃×#41	—	7	8	no	—
142	C₂×C₃×Q₈	—	7	1	no	—
143	C₂×C₃×D₄	—	7	2	no	—
144	C₂×C₃×D₄	—	7	1	no	—
145	C₂²×C₃×C₄	—	7	1	no	—
146	C₂²×C₃×C₄	—	7	2	no	—
147	C₂²×C₃×C₄	—	7	1	no	—
148	C₂²×C₃×C₄	—	7	1	no	—
149	C₂²×C₃×C₄	—	7	2	no	—
150	C₂²×C₃×C₄	—	7	2	no	—
151	C₃×C₄⋊C₄	—	7	2	no	—
152	C₃×C₄⋊C₄	—	7	2	no	—
153	C₃×C₄⋊C₄	—	7	1	no	—
154	C₃×C₄⋊C₄	—	7	1	no	—
155	C₃×C₂²⋊C₄	—	7	2	no	—
156	C₃×C₂²⋊C₄	—	7	2	no	—
157	C₃×C₂²⋊C₄	—	7	2	no	—
158	C₃×C₄²	—	7	1	no	—
159	C₃×C₄²	—	7	1	no	—
160	C₃×C₄²	—	7	2	no	—
161	C₃×C₄²	—	7	2	no	—
162	C₃×C₄²	—	7	1	no	—
163	C₃×C₄²	—	7	2	no	—
164	C₃×C₄²	—	7	1	no	—
165	C₂×ΓL(1,𝔽₈)	—	2	4	no	—
166	C₂×ΓL(1,𝔽₈)	C₂³×C₄	1	1	yes	characteristic
167	C₂×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
168	C₂×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
169	AGL(1,𝔽₇)	—	2	2	no	—
170	C₂×#41	—	7	1	no	—
171	C₄×Q₈	—	7	1	no	—
172	C₄×Q₈	—	7	1	no	—
173	C₄×D₄	—	7	1	no	—
174	C₄×D₄	—	7	2	no	—
175	C₄×D₄	—	7	2	no	—
176	C₄×D₄	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
177	#117	—	7	1	no	—
178	#117	—	7	2	no	—
179	C₂×C₄²	—	7	2	no	—
180	C₂×C₄²	—	7	1	no	—
181	C₂²×C₇	—	2	2	no	—
182	C₂²×C₇	—	2	2	no	—
183	C₂²×C₇	C₂²×C₃×C₄	1	4	yes	—
184	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
185	C₂×D₇	—	2	1	no	—
186	C₂×D₇	—	2	1	no	—
187	C₂×D₇	C₂²×C₃×C₄	1	2	yes	—
188	C₄×C₇	—	2	1	no	—
189	C₄×C₇	—	2	2	no	—
190	C₄×C₇	C₂²×C₃×C₄	1	2	yes	—
191	C₄×C₇	C₃×#41	1	2	yes	complemented
192	Dic₇	—	2	1	no	—
193	Dic₇	—	2	2	no	—
194	Dic₇	C₂²×C₃×C₄	1	4	yes	—
195	Dic₇	C₂²×C₃×C₄	1	2	yes	—
196	Dic₇	C₃×#41	1	2	yes	complemented
197	C₂³×C₃	—	7	1	no	—
198	C₂³×C₃	—	7	2	no	—
199	C₃×Q₈	—	7	4	no	—
200	C₃×D₄	—	7	8	no	—
201	C₃×D₄	—	7	4	no	—
202	C₂×C₃×C₄	—	7	4	no	—
203	C₂×C₃×C₄	—	7	8	no	—
204	C₂×C₃×C₄	—	7	1	no	—
205	C₂×C₃×C₄	—	7	1	no	—
206	C₂×C₃×C₄	—	7	2	no	—
207	C₂×C₃×C₄	—	7	1	no	—
208	C₂×C₃×C₄	—	7	2	no	—
209	C₂×C₃×C₄	—	7	1	no	—
210	C₂×C₃×C₄	—	7	2	no	—
211	C₂×C₃×C₄	—	7	1	no	—
212	C₂×C₃×C₄	—	7	1	no	—
213	C₂×C₃×C₄	—	14	4	no	—
214	C₂×C₃×C₄	—	14	2	no	—
215	C₂×C₃×C₄	—	14	2	no	—
216	C₂×C₃×C₄	—	14	4	no	—
217	ΓL(1,𝔽₈)	C₄×#41	1	1	yes	characteristic, complemented, Hall
218	#41	—	7	8	no	—
219	C₂×Q₈	—	7	1	no	—
220	C₂×D₄	—	7	2	no	—
221	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
222	C₂²×C₄	—	7	2	no	—
223	C₂²×C₄	—	7	1	no	—
224	C₂²×C₄	—	7	2	no	—
225	C₂²×C₄	—	7	1	no	—
226	C₂²×C₄	—	7	1	no	—
227	C₂²×C₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
228	C₄⋊C₄	—	7	2	no	—
229	C₄⋊C₄	—	7	2	no	—
230	C₄⋊C₄	—	7	1	no	—
231	C₄⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
232	C₂²⋊C₄	—	7	2	no	—
233	C₂²⋊C₄	—	7	2	no	—
234	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
235	C₄²	—	7	2	no	—
236	C₄²	—	7	1	no	—
237	C₄²	—	7	2	no	—
238	C₄²	—	7	1	no	—
239	C₄²	—	7	1	no	—
240	C₄²	—	7	2	no	—
241	C₄²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
242	C₂×C₇	—	2	4	no	—
243	C₂×C₇	C₂³×C₃×C₄	1	1	yes	characteristic
244	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
245	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
246	D₇	—	2	2	no	—
247	C₂²×C₃	—	7	2	no	—
248	C₂²×C₃	—	7	4	no	—
249	C₂²×C₃	—	7	1	no	—
250	C₂²×C₃	—	14	2	no	—
251	C₂²×C₃	—	14	2	no	—
252	C₂²×C₃	—	14	1	no	—
253	C₂²×C₃	—	14	1	no	—
254	C₃×C₄	—	7	2	no	—
255	C₃×C₄	—	7	4	no	—
256	C₃×C₄	—	7	2	no	—
257	C₃×C₄	—	7	2	no	—
258	C₃×C₄	—	7	2	no	—
259	C₃×C₄	—	14	2	no	—
260	C₃×C₄	—	14	1	no	—
261	C₃×C₄	—	14	1	no	—
262	C₃×C₄	—	14	2	no	—
263	C₂³	—	7	1	no	—
264	C₂³	C₂²×AGL(1,𝔽₇)	1	2	yes	—
265	Q₈	—	7	4	no	—
266	D₄	—	7	8	no	—
267	D₄	C₄×AGL(1,𝔽₇)	1	4	yes	complemented
268	C₂×C₄	—	2	4	no	—
269	C₂×C₄	—	7	8	no	—
270	C₂×C₄	—	7	1	no	—
271	C₂×C₄	—	7	1	no	—
272	C₂×C₄	—	7	2	no	—
273	C₂×C₄	—	7	4	no	—
274	C₂×C₄	—	7	1	no	—
275	C₂×C₄	—	7	2	no	—
276	C₂×C₄	—	14	2	no	—
277	C₂×C₄	—	14	4	no	—
278	C₂×C₄	—	14	2	no	—
279	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
280	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
281	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
282	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
283	C₇	C₃×C₄×#41	1	1	yes	characteristic, complemented, Sylow
284	C₂×C₃	—	7	1	no	—
285	C₂×C₃	—	7	1	no	—
286	C₂×C₃	—	7	1	no	—
287	C₂×C₃	—	14	4	no	—
288	C₂×C₃	—	14	2	no	—
289	C₂²	—	2	2	no	—
290	C₂²	—	2	2	no	—
291	C₂²	—	7	2	no	—
292	C₂²	—	14	1	no	—
293	C₂²	—	14	1	no	—
294	C₂²	C₂×C₄×AGL(1,𝔽₇)	1	4	yes	—
295	C₂²	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
296	C₄	—	2	2	no	—
297	C₄	—	2	1	no	—
298	C₄	—	7	2	no	—
299	C₄	—	7	4	no	—
300	C₄	—	7	2	no	—
301	C₄	—	14	1	no	—
302	C₄	—	14	2	no	—
303	C₄	C₂×C₄×AGL(1,𝔽₇)	1	2	yes	—
304	C₄	#1159⋊C₃	1	2	yes	direct product factor
305	C₃	—	7	1	no	Sylow
306	C₂	—	2	4	no	—
307	C₂	—	14	2	no	—
308	C₂	C₂²×C₄×AGL(1,𝔽₇)	1	1	yes	characteristic
309	C₂	C₂×#1159⋊C₃	1	1	yes	characteristic
310	C₂	#41×AGL(1,𝔽₇)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×AGL(1,𝔽₇)
commutator	C₂×C₇	C₂³×C₃×C₄
Frattini	C₂²	C₂³×AGL(1,𝔽₇)
Fitting	C₄×C₇×D₄	C₂×C₃
socle, cosocle	C₂²×C₇	C₂⁴×C₃
prime radical	C₂×#1159⋊C₃	C₂
hypercenter	C₄×D₄	AGL(1,𝔽₇)
hypocenter	C₇	C₃×C₄×#41
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₄×D₄×ΓL(1,𝔽₈)	C₂	semidirect
3. D₄×ΓL(1,𝔽₈)⋊C₄	C₂	semidirect
4. C₄×(C₂²⋊D₇)⋊C₃	C₂	semidirect
5. C₂×C₄×ΓL(1,𝔽₈)⋊C₄	C₂	semidirect
6. #6455⋊C₃	C₂	semidirect
7. #6450⋊C₃	C₂	semidirect
8. ((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	semidirect
9. #6440⋊C₃	C₂	semidirect
10. C₄²×AGL(1,𝔽₇)	C₂	semidirect
11. C₄×ΓL(1,𝔽₈)⋊Q₈	C₂	semidirect
12. C₄×#1159	C₃	semidirect
18. #1159⋊C₃	C₄	direct (N × H)
38. C₄×C₇×D₄	C₂×C₃	semidirect
39. D₄×Dic₇	C₂×C₃	semidirect
40. C₄×C₂²⋊D₇	C₂×C₃	semidirect
41. C₂×C₄×Dic₇	C₂×C₃	semidirect
42. #6455	C₂×C₃	semidirect
43. #6450	C₂×C₃	semidirect
44. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
45. #6440	C₂×C₃	semidirect
46. C₄²×D₇	C₂×C₃	semidirect
47. C₄×Dic₁₄	C₂×C₃	semidirect
51. D₄×ΓL(1,𝔽₈)	C₂×C₄	semidirect
57. (C₂²⋊D₇)⋊C₃	C₂×C₄	semidirect
59. C₂×ΓL(1,𝔽₈)⋊C₄	C₂×C₄	semidirect
67. C₄×AGL(1,𝔽₇)	C₂×C₄	semidirect
68. ΓL(1,𝔽₈)⋊Q₈	C₂×C₄	semidirect
74. #1159	C₃×C₄	semidirect
114. C₄×ΓL(1,𝔽₈)	#41	semidirect
119. ΓL(1,𝔽₈)⋊C₄	#41	semidirect
123. C₇×D₄	C₂×C₃×C₄	semidirect
129. C₂²⋊D₇	C₂×C₃×C₄	semidirect
131. C₂×Dic₇	C₂×C₃×C₄	semidirect
139. C₄×D₇	C₂×C₃×C₄	semidirect
140. Dic₁₄	C₂×C₃×C₄	semidirect
176. C₄×D₄	AGL(1,𝔽₇)	semidirect
191. C₄×C₇	C₃×#41	semidirect
196. Dic₇	C₃×#41	semidirect
217. ΓL(1,𝔽₈)	C₄×#41	semidirect
267. D₄	C₄×AGL(1,𝔽₇)	semidirect
283. C₇	C₃×C₄×#41	semidirect
304. C₄	#1159⋊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
C₂×#1159⋊C₃	2
C₄×D₄×ΓL(1,𝔽₈)	2
D₄×ΓL(1,𝔽₈)⋊C₄	2
C₄×(C₂²⋊D₇)⋊C₃	2
C₂×C₄×ΓL(1,𝔽₈)⋊C₄	2
#6455⋊C₃	2
#6450⋊C₃	2
((C₂²⋊D₇)⋊C₃)⋊C₄	2
#6440⋊C₃	2
C₄²×AGL(1,𝔽₇)	2
C₄×ΓL(1,𝔽₈)⋊Q₈	2
C₄×#1159	3
C₃×C₄×#41	7

Subgroups — C4×#1159⋊C3 #13057282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#1159⋊C₃ #13057282