Subgroups — #90323⋊C₃ #13057356

Order 1344.

560 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×ΓL(1,𝔽₈)⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#6507⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×(C₂²⋊D₇)⋊C₃	C₂	1	1	yes	maximal, characteristic
6	#6460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#6459⋊C₃	C₂	1	2	yes	maximal, complemented
8	#6451⋊C₃	C₂	1	2	yes	maximal, complemented
9	#6450⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂	1	2	yes	maximal
11	#6441⋊C₃	C₂	1	2	yes	maximal, complemented
12	#90323	C₃	1	1	yes	maximal, characteristic, complemented, Hall
13	C₂×Q₈×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
14	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
15	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic
16	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
17	Q₈×AGL(1,𝔽₇)	—	2	4	no	—
18	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	—
19	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
20	C₂×ΓL(1,𝔽₈)⋊Q₈	—	2	4	no	—
21	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	2	yes	—
22	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	2	yes	—
23	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	1	yes	characteristic
25	C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
26	C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
27	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
28	(C₂²⋊Dic₇)⋊C₃	C₂²	1	1	yes	characteristic
29	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	—
30	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic
31	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	2	yes	—
32	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	—
33	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	—
34	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	2	yes	—
35	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	—
37	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×Q₈×D₇	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×Dic₁₄	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
41	#6507	C₂×C₃	1	1	yes	characteristic, complemented
42	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic
43	#6460	C₂×C₃	1	1	yes	characteristic, complemented
44	#6459	C₂×C₃	1	2	yes	complemented
45	#6451	C₂×C₃	1	2	yes	complemented
46	#6450	C₂×C₃	1	1	yes	characteristic, complemented
47	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	—
48	#6441	C₂×C₃	1	2	yes	complemented
49	C₃×D₄×Q₈	—	7	1	no	maximal, Hall
50	C₂³×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
51	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
52	Q₈×ΓL(1,𝔽₈)	—	2	2	no	—
53	C₂×C₄×ΓL(1,𝔽₈)	—	2	2	no	—
54	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
55	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
56	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
57	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
58	(C₂²⋊D₇)⋊C₃	Q₈	1	4	yes	complemented
59	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	4	no	—
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	1	yes	characteristic
63	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
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	4	no	—
67	ΓL(1,𝔽₈)⋊Q₈	—	2	2	no	—
68	ΓL(1,𝔽₈)⋊Q₈	—	2	4	no	—
69	ΓL(1,𝔽₈)⋊Q₈	—	2	4	no	—
70	ΓL(1,𝔽₈)⋊Q₈	D₄	1	4	yes	complemented
71	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
74	C₂²×Dic₇	C₂²×C₃	1	2	yes	—
75	Q₈×D₇	—	2	4	no	—
76	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
77	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
78	C₂×Dic₁₄	—	2	4	no	—
79	C₂×Dic₁₄	C₂²×C₃	1	2	yes	—
80	C₂×Dic₁₄	C₂²×C₃	1	2	yes	—
81	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
83	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
87	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
88	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₄⋊Dic₇	C₂²×C₃	1	2	yes	—
90	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
91	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
92	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
93	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₄×Dic₇	C₂²×C₃	1	2	yes	—
95	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
96	C₂²×C₃×Q₈	—	7	1	no	—
97	C₂²×C₃×Q₈	—	7	1	no	—
98	C₃×C₄⋊Q₈	—	7	2	no	—
99	C₃×C₄⋊Q₈	—	7	1	no	—
100	C₃×C₂²⋊Q₈	—	7	2	no	—
101	C₃×C₂²⋊Q₈	—	7	2	no	—
102	C₃×C₂²⋊Q₈	—	7	1	no	—
103	C₃×C₂²⋊Q₈	—	7	1	no	—
104	C₃×C₄×Q₈	—	7	1	no	—
105	C₃×C₄×D₄	—	7	2	no	—
106	C₃×C₄×D₄	—	7	1	no	—
107	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
108	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
109	C₂²×ΓL(1,𝔽₈)	C₂×Q₈	1	2	yes	complemented
110	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
111	C₂×AGL(1,𝔽₇)	—	2	1	no	—
112	C₂×AGL(1,𝔽₇)	—	2	1	no	—
113	C₂×AGL(1,𝔽₇)	C₂×Q₈	1	2	yes	complemented
114	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
115	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
116	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
117	C₄×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	—
118	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
119	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
120	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
121	ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	4	yes	—
122	ΓL(1,𝔽₈)⋊C₄	C₂×Q₈	1	2	yes	complemented
123	D₄×Q₈	—	7	1	no	Sylow
124	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
125	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
126	C₇×Q₈	—	2	2	no	—
127	C₂×C₄×C₇	—	2	2	no	—
128	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
129	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
130	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
131	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
132	C₂²⋊D₇	C₃×Q₈	1	4	yes	complemented
133	C₂×Dic₇	—	2	4	no	—
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	C₂×Dic₇	C₂³×C₃	1	2	yes	—
138	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
139	C₄×D₇	—	2	2	no	—
140	C₄×D₇	—	2	4	no	—
141	Dic₁₄	—	2	2	no	—
142	Dic₁₄	—	2	4	no	—
143	Dic₁₄	—	2	4	no	—
144	Dic₁₄	C₃×D₄	1	4	yes	complemented
145	C₂×C₃×Q₈	—	7	1	no	—
146	C₂×C₃×Q₈	—	7	2	no	—
147	C₂×C₃×Q₈	—	7	2	no	—
148	C₂×C₃×Q₈	—	7	1	no	—
149	C₂×C₃×Q₈	—	7	1	no	—
150	C₂×C₃×Q₈	—	14	4	no	—
151	C₂×C₃×Q₈	—	14	4	no	—
152	C₂×C₃×D₄	—	7	1	no	—
153	C₂²×C₃×C₄	—	7	2	no	—
154	C₂²×C₃×C₄	—	7	1	no	—
155	C₂²×C₃×C₄	—	7	2	no	—
156	C₂²×C₃×C₄	—	7	1	no	—
157	C₃×C₄⋊C₄	—	7	2	no	—
158	C₃×C₄⋊C₄	—	7	1	no	—
159	C₃×C₄⋊C₄	—	7	2	no	—
160	C₃×C₄⋊C₄	—	7	2	no	—
161	C₃×C₄⋊C₄	—	7	2	no	—
162	C₃×C₄⋊C₄	—	7	1	no	—
163	C₃×C₄⋊C₄	—	7	2	no	—
164	C₃×C₂²⋊C₄	—	7	1	no	—
165	C₃×C₂²⋊C₄	—	7	2	no	—
166	C₃×C₂²⋊C₄	—	7	1	no	—
167	C₃×C₂²⋊C₄	—	7	2	no	—
168	C₃×C₄²	—	7	2	no	—
169	C₃×C₄²	—	7	1	no	—
170	C₂×ΓL(1,𝔽₈)	—	2	2	no	—
171	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
172	C₂×ΓL(1,𝔽₈)	C₂²×Q₈	1	1	yes	characteristic
173	C₂×ΓL(1,𝔽₈)	2₋¹⁺⁴	1	1	yes	characteristic
174	AGL(1,𝔽₇)	—	2	2	no	—
175	C₂²×Q₈	—	7	1	no	—
176	C₂²×Q₈	—	7	1	no	—
177	C₄⋊Q₈	—	7	1	no	—
178	C₄⋊Q₈	—	7	2	no	—
179	C₂²⋊Q₈	—	7	2	no	—
180	C₂²⋊Q₈	—	7	1	no	—
181	C₂²⋊Q₈	—	7	2	no	—
182	C₂²⋊Q₈	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
183	C₄×Q₈	—	7	1	no	—
184	C₄×D₄	—	7	1	no	—
185	C₄×D₄	—	7	2	no	—
186	C₂²×C₇	—	2	1	no	—
187	C₂²×C₇	—	2	1	no	—
188	C₂²×C₇	C₂×C₃×Q₈	1	2	yes	complemented
189	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
190	C₂×D₇	—	2	1	no	—
191	C₂×D₇	—	2	1	no	—
192	C₂×D₇	C₂×C₃×Q₈	1	2	yes	complemented
193	C₄×C₇	—	2	1	no	—
194	C₄×C₇	—	2	2	no	—
195	C₄×C₇	—	2	2	no	—
196	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
197	Dic₇	—	2	1	no	—
198	Dic₇	—	2	2	no	—
199	Dic₇	—	2	1	no	—
200	Dic₇	C₂×C₃×D₄	1	4	yes	—
201	Dic₇	C₂×C₃×Q₈	1	2	yes	complemented
202	C₂³×C₃	—	7	1	no	—
203	C₂³×C₃	—	7	1	no	—
204	C₃×Q₈	—	7	4	no	—
205	C₃×Q₈	—	14	2	no	—
206	C₃×Q₈	—	14	4	no	—
207	C₃×Q₈	—	14	4	no	—
208	C₃×Q₈	—	14	2	no	—
209	C₃×D₄	—	7	4	no	—
210	C₂×C₃×C₄	—	7	1	no	—
211	C₂×C₃×C₄	—	7	2	no	—
212	C₂×C₃×C₄	—	7	1	no	—
213	C₂×C₃×C₄	—	7	1	no	—
214	C₂×C₃×C₄	—	7	2	no	—
215	C₂×C₃×C₄	—	7	1	no	—
216	C₂×C₃×C₄	—	7	2	no	—
217	C₂×C₃×C₄	—	7	1	no	—
218	C₂×C₃×C₄	—	7	2	no	—
219	C₂×C₃×C₄	—	14	2	no	—
220	C₂×C₃×C₄	—	14	4	no	—
221	C₂×C₃×C₄	—	14	2	no	—
222	C₂×C₃×C₄	—	14	4	no	—
223	ΓL(1,𝔽₈)	D₄×Q₈	1	1	yes	characteristic, complemented, Hall
224	C₂×Q₈	—	7	1	no	—
225	C₂×Q₈	—	7	2	no	—
226	C₂×Q₈	—	7	2	no	—
227	C₂×Q₈	—	7	1	no	—
228	C₂×Q₈	—	14	4	no	—
229	C₂×Q₈	—	14	4	no	—
230	C₂×Q₈	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
231	C₂×D₄	—	7	1	no	—
232	C₂²×C₄	—	7	2	no	—
233	C₂²×C₄	—	7	2	no	—
234	C₂²×C₄	—	7	1	no	—
235	C₂²×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
236	C₄⋊C₄	—	7	1	no	—
237	C₄⋊C₄	—	7	2	no	—
238	C₄⋊C₄	—	7	2	no	—
239	C₄⋊C₄	—	7	2	no	—
240	C₄⋊C₄	—	7	2	no	—
241	C₄⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
242	C₄⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
243	C₂²⋊C₄	—	7	1	no	—
244	C₂²⋊C₄	—	7	1	no	—
245	C₂²⋊C₄	—	7	2	no	—
246	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	—
247	C₄²	—	7	2	no	—
248	C₄²	—	7	1	no	—
249	C₂×C₇	—	2	2	no	—
250	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
251	C₂×C₇	C₂²×C₃×Q₈	1	1	yes	characteristic
252	C₂×C₇	C₃×2₋¹⁺⁴	1	1	yes	characteristic
253	D₇	—	2	2	no	—
254	C₂²×C₃	—	7	2	no	—
255	C₂²×C₃	—	7	2	no	—
256	C₂²×C₃	—	7	1	no	—
257	C₂²×C₃	—	14	1	no	—
258	C₂²×C₃	—	14	1	no	—
259	C₂²×C₃	—	14	1	no	—
260	C₂²×C₃	—	14	1	no	—
261	C₃×C₄	—	7	4	no	—
262	C₃×C₄	—	7	2	no	—
263	C₃×C₄	—	7	2	no	—
264	C₃×C₄	—	14	1	no	—
265	C₃×C₄	—	14	2	no	—
266	C₃×C₄	—	14	2	no	—
267	C₃×C₄	—	14	1	no	—
268	C₃×C₄	—	14	2	no	—
269	C₃×C₄	—	14	1	no	—
270	C₂³	—	7	1	no	—
271	C₂³	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
272	Q₈	—	2	2	no	—
273	Q₈	—	7	4	no	—
274	Q₈	—	14	4	no	—
275	Q₈	—	14	4	no	—
276	Q₈	—	14	2	no	—
277	D₄	—	7	4	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	7	1	no	—
280	C₂×C₄	—	7	2	no	—
281	C₂×C₄	—	7	1	no	—
282	C₂×C₄	—	7	1	no	—
283	C₂×C₄	—	7	2	no	—
284	C₂×C₄	—	14	4	no	—
285	C₂×C₄	—	14	4	no	—
286	C₂×C₄	—	14	2	no	—
287	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
288	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
289	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
290	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
291	C₇	C₃×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
292	C₂×C₃	—	7	1	no	—
293	C₂×C₃	—	7	1	no	—
294	C₂×C₃	—	7	1	no	—
295	C₂×C₃	—	14	2	no	—
296	C₂×C₃	—	14	2	no	—
297	C₂²	—	2	1	no	—
298	C₂²	—	2	1	no	—
299	C₂²	—	7	2	no	—
300	C₂²	—	14	1	no	—
301	C₂²	—	14	1	no	—
302	C₂²	Q₈×AGL(1,𝔽₇)	1	2	yes	complemented
303	C₂²	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
304	C₄	—	2	1	no	—
305	C₄	—	2	2	no	—
306	C₄	—	2	2	no	—
307	C₄	—	7	4	no	—
308	C₄	—	7	2	no	—
309	C₄	—	14	2	no	—
310	C₄	—	14	1	no	—
311	C₄	—	14	1	no	—
312	C₄	D₄×AGL(1,𝔽₇)	1	2	yes	—
313	C₃	—	7	1	no	Sylow
314	C₂	—	2	2	no	—
315	C₂	—	14	2	no	—
316	C₂	C₂×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
317	C₂	C₂×Q₈×AGL(1,𝔽₇)	1	1	yes	characteristic
318	C₂	#10621519	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₇	C₂⁴×C₃
Fitting	C₇×C₂²⋊Q₈	C₂×C₃
prime radical	C₂×(C₂²⋊D₇)⋊C₃	C₂²
hypercenter	C₂²⋊Q₈	AGL(1,𝔽₇)
hypocenter	C₇	C₃×D₄×Q₈
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×AGL(1,𝔽₇)	C₂	semidirect
2. C₂²×ΓL(1,𝔽₈)⋊Q₈	C₂	semidirect
3. ΓL(1,𝔽₈)×C₂²⋊Q₈	C₂	semidirect
4. #6507⋊C₃	C₂	semidirect
6. #6460⋊C₃	C₂	semidirect
7. #6459⋊C₃	C₂	semidirect
8. #6451⋊C₃	C₂	semidirect
9. #6450⋊C₃	C₂	semidirect
11. #6441⋊C₃	C₂	semidirect
12. #90323	C₃	semidirect
38. C₂×Q₈×D₇	C₂×C₃	semidirect
39. C₂²×Dic₁₄	C₂×C₃	semidirect
40. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
41. #6507	C₂×C₃	semidirect
43. #6460	C₂×C₃	semidirect
44. #6459	C₂×C₃	semidirect
45. #6451	C₂×C₃	semidirect
46. #6450	C₂×C₃	semidirect
48. #6441	C₂×C₃	semidirect
58. (C₂²⋊D₇)⋊C₃	Q₈	semidirect
70. ΓL(1,𝔽₈)⋊Q₈	D₄	semidirect
109. C₂²×ΓL(1,𝔽₈)	C₂×Q₈	semidirect
113. C₂×AGL(1,𝔽₇)	C₂×Q₈	semidirect
122. ΓL(1,𝔽₈)⋊C₄	C₂×Q₈	semidirect
132. C₂²⋊D₇	C₃×Q₈	semidirect
144. Dic₁₄	C₃×D₄	semidirect
182. C₂²⋊Q₈	AGL(1,𝔽₇)	semidirect
188. C₂²×C₇	C₂×C₃×Q₈	semidirect
192. C₂×D₇	C₂×C₃×Q₈	semidirect
201. Dic₇	C₂×C₃×Q₈	semidirect
223. ΓL(1,𝔽₈)	D₄×Q₈	semidirect
291. C₇	C₃×D₄×Q₈	semidirect
302. C₂²	Q₈×AGL(1,𝔽₇)	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×AGL(1,𝔽₇)	2
C₂²×ΓL(1,𝔽₈)⋊Q₈	2
ΓL(1,𝔽₈)×C₂²⋊Q₈	2
#6507⋊C₃	2
C₄×(C₂²⋊D₇)⋊C₃	2
#6460⋊C₃	2
#6459⋊C₃	2
#6451⋊C₃	2
#6450⋊C₃	2
((C₂²⋊D₇)⋊C₃)⋊C₄	2
#6441⋊C₃	2
#90323	3
C₃×D₄×Q₈	7

Subgroups — #90323⋊C3 #13057356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #90323⋊C₃ #13057356