Subgroups — C₈×AGL(1,ℤ/8)×C₁₀₇ #41043814

Order 27392.

802 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#41×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×AGL(1,ℤ/8)×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#1580	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₈×SD₁₆×C₁₀₇	C₂	1	2	yes	maximal, complemented
7	C₈×D₈×C₁₀₇	C₂	1	2	yes	maximal, complemented
8	C₁₀₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₁₀₇	C₄	1	1	yes	characteristic
13	C₂³×C₈×C₁₀₇	—	2	1	no	—
14	C₄×#41×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
16	C₈×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
17	C₈×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
18	#442×C₁₀₇	C₄	1	2	yes	—
19	#440×C₁₀₇	C₄	1	2	yes	—
20	C₄×SD₁₆×C₁₀₇	C₂²	1	2	yes	—
21	C₄×D₈×C₁₀₇	C₂²	1	2	yes	—
22	C₈×D₄×C₁₀₇	—	2	1	no	—
23	C₈×D₄×C₁₀₇	—	2	1	no	—
24	C₈×D₄×C₁₀₇	—	2	1	no	—
25	C₈×D₄×C₁₀₇	—	2	1	no	—
26	C₈×D₄×C₁₀₇	C₂²	1	2	yes	—
27	C₈×D₄×C₁₀₇	C₂²	1	2	yes	—
28	C₈×D₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
29	C₈×D₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
30	#431×C₁₀₇	—	2	1	no	—
31	#431×C₁₀₇	C₂²	1	1	yes	characteristic
32	#431×C₁₀₇	C₂²	1	1	yes	characteristic
33	#428×C₁₀₇	C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
35	#418×C₁₀₇	C₄	1	1	yes	characteristic
36	#417×C₁₀₇	C₄	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₁₀₇	—	2	1	no	—
38	C₄×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₀₇	—	2	1	no	—
40	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
41	#335×C₁₀₇	C₂²	1	2	yes	complemented
42	#334×C₁₀₇	C₂²	1	2	yes	complemented
43	Q₈⋊C₈×C₁₀₇	C₂²	1	2	yes	complemented
44	D₄⋊C₈×C₁₀₇	C₂²	1	2	yes	—
45	D₄⋊C₈×C₁₀₇	C₂²	1	2	yes	—
46	D₄⋊C₈×C₁₀₇	C₂²	1	2	yes	complemented
47	#322×C₁₀₇	C₂²	1	2	yes	complemented
48	C₈²×C₁₀₇	C₂²	1	2	yes	complemented
49	C₂×#41×C₁₀₇	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₀₇	—	2	1	no	—
52	AGL(1,ℤ/8)×C₁₀₇	C₈	1	8	yes	direct product factor
53	C₂×SD₁₆×C₁₀₇	C₂×C₄	1	2	yes	—
54	C₂×D₈×C₁₀₇	C₂×C₄	1	2	yes	—
55	C₂×M₁₆×C₁₀₇	C₂×C₄	1	1	yes	characteristic
56	C₂×M₁₆×C₁₀₇	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₀₇	—	2	1	no	—
58	C₂²×C₈×C₁₀₇	—	2	1	no	—
59	C₂²×C₈×C₁₀₇	—	2	2	no	—
60	C₂²×C₈×C₁₀₇	—	2	1	no	—
61	C₂²×C₈×C₁₀₇	—	2	2	no	—
62	C₂²×C₈×C₁₀₇	—	4	4	no	—
63	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
66	C₄×Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₁₀₇	—	2	1	no	—
68	C₄×D₄×C₁₀₇	—	2	1	no	—
69	C₄×D₄×C₁₀₇	—	2	1	no	—
70	C₄×D₄×C₁₀₇	—	2	1	no	—
71	C₄×D₄×C₁₀₇	C₂×C₄	1	2	yes	—
72	C₄×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₀₇	C₂³	1	2	yes	—
74	C₄×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
75	#117×C₁₀₇	—	2	1	no	—
76	#117×C₁₀₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
79	C₂×C₄²×C₁₀₇	—	2	1	no	—
80	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
81	#107×C₁₀₇	C₂×C₄	1	2	yes	—
82	#106×C₁₀₇	C₂×C₄	1	2	yes	—
83	C₄⋊C₈×C₁₀₇	—	2	1	no	—
84	C₄⋊C₈×C₁₀₇	—	2	1	no	—
85	C₄⋊C₈×C₁₀₇	—	2	1	no	—
86	C₄⋊C₈×C₁₀₇	—	2	1	no	—
87	C₄⋊C₈×C₁₀₇	C₂³	1	2	yes	—
88	C₄⋊C₈×C₁₀₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₁₀₇	C₂³	1	1	yes	characteristic
90	#103×C₁₀₇	C₂×C₄	1	2	yes	—
91	#102×C₁₀₇	C₂×C₄	1	2	yes	—
92	#102×C₁₀₇	C₂×C₄	1	2	yes	—
93	#102×C₁₀₇	C₂×C₄	1	2	yes	—
94	C₂²⋊C₈×C₁₀₇	—	2	1	no	—
95	C₂²⋊C₈×C₁₀₇	—	2	1	no	—
96	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
97	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
98	C₂²⋊C₈×C₁₀₇	—	2	1	no	—
99	C₂²⋊C₈×C₁₀₇	—	2	1	no	—
100	#97×C₁₀₇	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₁₀₇	—	2	1	no	—
102	C₄×C₈×C₁₀₇	—	2	1	no	—
103	C₄×C₈×C₁₀₇	—	2	1	no	—
104	C₄×C₈×C₁₀₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₁₀₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
107	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
108	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
110	C₂⁴×C₁₀₇	—	2	1	no	—
111	#41×C₁₀₇	—	2	2	no	—
112	#41×C₁₀₇	C₂×C₈	1	4	yes	complemented
113	C₂×Q₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₁₀₇	—	2	1	no	—
115	C₂×D₄×C₁₀₇	—	2	1	no	—
116	C₂×D₄×C₁₀₇	—	2	2	no	—
117	C₂×D₄×C₁₀₇	C₂×C₈	1	4	yes	complemented
118	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
119	C₂×D₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₀₇	—	2	1	no	—
121	C₂²×C₄×C₁₀₇	—	2	1	no	—
122	C₂²×C₄×C₁₀₇	—	2	1	no	—
123	C₂²×C₄×C₁₀₇	—	2	2	no	—
124	C₂²×C₄×C₁₀₇	—	2	1	no	—
125	C₂²×C₄×C₁₀₇	—	2	2	no	—
126	C₂²×C₄×C₁₀₇	—	4	2	no	—
127	C₂²×C₄×C₁₀₇	—	4	2	no	—
128	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
131	SD₁₆×C₁₀₇	C₂×C₈	1	8	yes	complemented
132	D₈×C₁₀₇	C₂×C₈	1	8	yes	complemented
133	M₁₆×C₁₀₇	—	2	2	no	—
134	M₁₆×C₁₀₇	C₂×C₈	1	4	yes	complemented
135	C₂×C₈×C₁₀₇	—	2	2	no	—
136	C₂×C₈×C₁₀₇	—	2	1	no	—
137	C₂×C₈×C₁₀₇	—	2	1	no	—
138	C₂×C₈×C₁₀₇	—	2	2	no	—
139	C₂×C₈×C₁₀₇	—	2	2	no	—
140	C₂×C₈×C₁₀₇	—	4	1	no	—
141	C₂×C₈×C₁₀₇	—	4	2	no	—
142	C₂×C₈×C₁₀₇	—	4	4	no	—
143	C₂×C₈×C₁₀₇	—	4	2	no	—
144	C₂×C₈×C₁₀₇	—	4	2	no	—
145	C₂×C₈×C₁₀₇	—	4	4	no	—
146	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₁₀₇	—	2	1	no	—
153	C₄⋊C₄×C₁₀₇	—	2	1	no	—
154	C₄⋊C₄×C₁₀₇	—	2	1	no	—
155	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
157	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
158	C₂²⋊C₄×C₁₀₇	—	2	1	no	—
159	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
160	C₂²⋊C₄×C₁₀₇	—	2	1	no	—
161	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
162	C₂²⋊C₄×C₁₀₇	—	2	1	no	—
163	C₄²×C₁₀₇	—	2	1	no	—
164	C₄²×C₁₀₇	—	2	1	no	—
165	C₄²×C₁₀₇	—	2	1	no	—
166	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₀₇	#41	1	1	yes	characteristic
169	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
170	C₂³×C₁₀₇	—	2	1	no	—
171	C₂³×C₁₀₇	—	2	2	no	—
172	C₂³×C₁₀₇	—	2	4	no	—
173	C₂³×C₁₀₇	—	4	2	no	—
174	C₂³×C₁₀₇	—	4	2	no	—
175	C₂³×C₁₀₇	C₄×D₄	1	1	yes	characteristic
176	Q₈×C₁₀₇	—	2	1	no	—
177	Q₈×C₁₀₇	C₂²×C₈	1	2	yes	complemented
178	D₄×C₁₀₇	—	2	4	no	—
179	D₄×C₁₀₇	—	2	2	no	—
180	D₄×C₁₀₇	—	2	1	no	—
181	D₄×C₁₀₇	—	2	4	no	—
182	D₄×C₁₀₇	C₂²×C₈	1	4	yes	—
183	D₄×C₁₀₇	C₂²×C₈	1	2	yes	complemented
184	C₂×C₄×C₁₀₇	—	2	1	no	—
185	C₂×C₄×C₁₀₇	—	2	1	no	—
186	C₂×C₄×C₁₀₇	—	2	1	no	—
187	C₂×C₄×C₁₀₇	—	2	4	no	—
188	C₂×C₄×C₁₀₇	—	2	1	no	—
189	C₂×C₄×C₁₀₇	—	2	1	no	—
190	C₂×C₄×C₁₀₇	—	2	2	no	—
191	C₂×C₄×C₁₀₇	—	4	1	no	—
192	C₂×C₄×C₁₀₇	—	4	2	no	—
193	C₂×C₄×C₁₀₇	—	4	4	no	—
194	C₂×C₄×C₁₀₇	—	4	2	no	—
195	C₂×C₄×C₁₀₇	—	4	2	no	—
196	C₂×C₄×C₁₀₇	—	4	1	no	—
197	C₂×C₄×C₁₀₇	—	4	1	no	—
198	C₂×C₄×C₁₀₇	—	4	2	no	—
199	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₀₇	C₂²×C₈	1	2	yes	—
203	C₂×C₄×C₁₀₇	#131	1	2	yes	—
204	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
207	C₈×C₁₀₇	—	2	2	no	—
208	C₈×C₁₀₇	—	2	1	no	—
209	C₈×C₁₀₇	—	2	1	no	—
210	C₈×C₁₀₇	—	2	1	no	—
211	C₈×C₁₀₇	—	4	2	no	—
212	C₈×C₁₀₇	—	4	1	no	—
213	C₈×C₁₀₇	—	4	2	no	—
214	C₈×C₁₀₇	—	4	1	no	—
215	C₈×C₁₀₇	C₂²×C₈	1	4	yes	complemented
216	C₈×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	direct product factor
217	C₂²×C₁₀₇	—	2	1	no	—
218	C₂²×C₁₀₇	—	2	1	no	—
219	C₂²×C₁₀₇	—	2	2	no	—
220	C₂²×C₁₀₇	—	2	4	no	—
221	C₂²×C₁₀₇	—	4	8	no	—
222	C₂²×C₁₀₇	—	4	2	no	—
223	C₂²×C₁₀₇	—	4	1	no	—
224	C₂²×C₁₀₇	—	4	1	no	—
225	C₂²×C₁₀₇	—	4	2	no	—
226	C₂²×C₁₀₇	C₈×D₄	1	2	yes	—
227	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
228	C₄×C₁₀₇	—	2	2	no	—
229	C₄×C₁₀₇	—	2	1	no	—
230	C₄×C₁₀₇	—	2	1	no	—
231	C₄×C₁₀₇	—	2	1	no	—
232	C₄×C₁₀₇	—	4	1	no	—
233	C₄×C₁₀₇	—	4	2	no	—
234	C₄×C₁₀₇	—	4	1	no	—
235	C₄×C₁₀₇	C₈×D₄	1	2	yes	—
236	C₄×C₁₀₇	C₂³×C₈	1	1	yes	characteristic
237	C₄×C₁₀₇	C₂×#131	1	1	yes	characteristic
238	C₄×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₄×C₁₀₇	#575	1	1	yes	characteristic
240	C₈×AGL(1,ℤ/8)	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂×C₁₀₇	—	2	2	no	—
242	C₂×C₁₀₇	—	4	2	no	—
243	C₂×C₁₀₇	—	4	4	no	—
244	C₂×C₁₀₇	C₂×C₈×D₄	1	1	yes	characteristic
245	C₂×C₁₀₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₂×C₁₀₇	#2955	1	1	yes	characteristic
247	C₈×#41	C₂×C₁₀₇	1	1	yes	characteristic, complemented
248	C₄×AGL(1,ℤ/8)	C₂×C₁₀₇	1	1	yes	characteristic
249	C₂×C₈×D₄	C₂×C₁₀₇	1	1	yes	characteristic, complemented
250	#1580	C₂×C₁₀₇	1	2	yes	complemented
251	SD₁₆⋊C₈	C₂×C₁₀₇	1	2	yes	complemented
252	C₈×SD₁₆	C₂×C₁₀₇	1	2	yes	complemented
253	C₈×D₈	C₂×C₁₀₇	1	2	yes	complemented
254	#1565	C₂×C₁₀₇	1	1	yes	characteristic, complemented
255	#1478	C₂×C₁₀₇	1	1	yes	characteristic, complemented
256	#1477	C₂×C₁₀₇	1	1	yes	characteristic, complemented
257	C₈×M₁₆	C₂×C₁₀₇	1	1	yes	characteristic, complemented
258	C₁₀₇	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×AGL(1,ℤ/8)	C₄×C₁₀₇	1	1	yes	characteristic
260	C₂³×C₈	—	2	1	no	—
261	C₄×#41	C₂²×C₁₀₇	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
263	C₈×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
264	C₈×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
265	#442	C₄×C₁₀₇	1	2	yes	—
266	#440	C₄×C₁₀₇	1	2	yes	—
267	C₄×SD₁₆	C₂²×C₁₀₇	1	2	yes	—
268	C₄×D₈	C₂²×C₁₀₇	1	2	yes	—
269	C₈×D₄	—	2	1	no	—
270	C₈×D₄	—	2	1	no	—
271	C₈×D₄	—	2	1	no	—
272	C₈×D₄	—	2	1	no	—
273	C₈×D₄	C₂²×C₁₀₇	1	2	yes	—
274	C₈×D₄	C₂²×C₁₀₇	1	2	yes	—
275	C₈×D₄	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
276	C₈×D₄	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
277	#431	—	2	1	no	—
278	#431	C₂²×C₁₀₇	1	1	yes	characteristic
279	#431	C₂²×C₁₀₇	1	1	yes	characteristic
280	#428	C₄×C₁₀₇	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
282	#418	C₄×C₁₀₇	1	1	yes	characteristic
283	#417	C₄×C₁₀₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	—	2	1	no	—
285	C₄×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
286	C₂×C₄×C₈	—	2	1	no	—
287	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
288	#335	C₂²×C₁₀₇	1	2	yes	complemented
289	#334	C₂²×C₁₀₇	1	2	yes	complemented
290	Q₈⋊C₈	C₂²×C₁₀₇	1	2	yes	complemented
291	D₄⋊C₈	C₂²×C₁₀₇	1	2	yes	—
292	D₄⋊C₈	C₂²×C₁₀₇	1	2	yes	—
293	D₄⋊C₈	C₂²×C₁₀₇	1	2	yes	complemented
294	#322	C₂²×C₁₀₇	1	2	yes	complemented
295	C₈²	C₂²×C₁₀₇	1	2	yes	complemented
296	C₂×#41	C₂×C₄×C₁₀₇	1	1	yes	characteristic
297	C₂²×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	AGL(1,ℤ/8)	C₈×C₁₀₇	1	8	yes	direct product factor
300	C₂×SD₁₆	C₂×C₄×C₁₀₇	1	2	yes	—
301	C₂×D₈	C₂×C₄×C₁₀₇	1	2	yes	—
302	C₂×M₁₆	C₂×C₄×C₁₀₇	1	1	yes	characteristic
303	C₂×M₁₆	C₂×C₄×C₁₀₇	1	1	yes	characteristic
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	4	4	no	—
310	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
311	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
312	C₄×Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
313	C₄×Q₈	C₂³×C₁₀₇	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	C₂×C₄×C₁₀₇	1	2	yes	—
319	C₄×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
320	C₄×D₄	C₂³×C₁₀₇	1	2	yes	—
321	C₄×D₄	C₂³×C₁₀₇	1	1	yes	characteristic
322	#117	—	2	1	no	—
323	#117	C₂×C₄×C₁₀₇	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
328	#107	C₂×C₄×C₁₀₇	1	2	yes	—
329	#106	C₂×C₄×C₁₀₇	1	2	yes	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	—	2	1	no	—
334	C₄⋊C₈	C₂³×C₁₀₇	1	1	yes	characteristic
335	C₄⋊C₈	C₂³×C₁₀₇	1	1	yes	characteristic
336	C₄⋊C₈	C₂³×C₁₀₇	1	2	yes	—
337	#103	C₂×C₄×C₁₀₇	1	2	yes	—
338	#102	C₂×C₄×C₁₀₇	1	2	yes	—
339	#102	C₂×C₄×C₁₀₇	1	2	yes	—
340	#102	C₂×C₄×C₁₀₇	1	2	yes	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	C₂²⋊C₈	—	2	2	no	—
345	C₂²⋊C₈	—	2	1	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	#97	C₂×C₄×C₁₀₇	1	2	yes	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	D₄×C₁₀₇	1	1	yes	characteristic
352	C₄×C₈	D₄×C₁₀₇	1	1	yes	characteristic
353	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
354	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
355	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
356	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
357	C₂⁴	—	2	1	no	—
358	#41	—	2	2	no	—
359	#41	C₂×C₈×C₁₀₇	1	4	yes	complemented
360	C₂×Q₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	C₂×C₈×C₁₀₇	1	4	yes	complemented
365	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
366	C₂×D₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
377	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
378	SD₁₆	C₂×C₈×C₁₀₇	1	8	yes	complemented
379	D₈	C₂×C₈×C₁₀₇	1	8	yes	complemented
380	M₁₆	—	2	2	no	—
381	M₁₆	C₂×C₈×C₁₀₇	1	4	yes	complemented
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	4	1	no	—
388	C₂×C₈	—	4	4	no	—
389	C₂×C₈	—	4	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	4	4	no	—
392	C₂×C₈	—	4	2	no	—
393	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
394	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
395	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
396	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
397	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
398	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
404	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
415	C₄²	#41×C₁₀₇	1	1	yes	characteristic
416	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
417	C₂³	—	2	4	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	C₄×D₄×C₁₀₇	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	C₂²×C₈×C₁₀₇	1	2	yes	complemented
425	D₄	—	2	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	1	no	—
429	D₄	C₂²×C₈×C₁₀₇	1	4	yes	—
430	D₄	C₂²×C₈×C₁₀₇	1	2	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
447	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
448	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
449	C₂×C₄	C₂²×C₈×C₁₀₇	1	2	yes	—
450	C₂×C₄	#131×C₁₀₇	1	2	yes	—
451	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	2	no	—
460	C₈	—	4	1	no	—
461	C₈	—	4	1	no	—
462	C₈	C₂²×C₈×C₁₀₇	1	4	yes	complemented
463	C₈	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	direct product factor
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	2	no	—
473	C₂²	C₈×D₄×C₁₀₇	1	2	yes	—
474	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	1	no	—
482	C₄	C₈×D₄×C₁₀₇	1	2	yes	—
483	C₄	C₂³×C₈×C₁₀₇	1	1	yes	characteristic
484	C₄	C₂×#131×C₁₀₇	1	1	yes	characteristic
485	C₄	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
486	C₄	#575×C₁₀₇	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	4	no	—
489	C₂	—	4	2	no	—
490	C₂	C₂×C₈×D₄×C₁₀₇	1	1	yes	characteristic
491	C₂	C₄×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
492	C₂	C₁₀₇×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₀₇	C₂×D₄
commutator	C₄	C₂³×C₈×C₁₀₇
Frattini, cosocle	C₄²	C₂⁴×C₁₀₇
socle	C₂²×C₁₀₇	C₂×C₄×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₁₀₇	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₀₇ ◁ C₂×C₄×C₈×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈×#41×C₁₀₇	C₂	semidirect
3. C₂×C₈×D₄×C₁₀₇	C₂	semidirect
4. C₁₀₇×#1580	C₂	semidirect
5. C₁₀₇×SD₁₆⋊C₈	C₂	semidirect
6. C₈×SD₁₆×C₁₀₇	C₂	semidirect
7. C₈×D₈×C₁₀₇	C₂	semidirect
8. C₁₀₇×#1565	C₂	semidirect
9. C₁₀₇×#1478	C₂	semidirect
10. C₁₀₇×#1477	C₂	semidirect
11. C₈×M₁₆×C₁₀₇	C₂	semidirect
16. C₈×Q₈×C₁₀₇	C₂²	semidirect
17. C₈×Q₈×C₁₀₇	C₂²	semidirect
28. C₈×D₄×C₁₀₇	C₂²	semidirect
29. C₈×D₄×C₁₀₇	C₂²	semidirect
41. #335×C₁₀₇	C₂²	semidirect
42. #334×C₁₀₇	C₂²	semidirect
43. Q₈⋊C₈×C₁₀₇	C₂²	semidirect
46. D₄⋊C₈×C₁₀₇	C₂²	semidirect
47. #322×C₁₀₇	C₂²	semidirect
48. C₈²×C₁₀₇	C₂²	semidirect
52. AGL(1,ℤ/8)×C₁₀₇	C₈	direct (N × H)
112. #41×C₁₀₇	C₂×C₈	semidirect
117. C₂×D₄×C₁₀₇	C₂×C₈	semidirect
131. SD₁₆×C₁₀₇	C₂×C₈	semidirect
132. D₈×C₁₀₇	C₂×C₈	semidirect
134. M₁₆×C₁₀₇	C₂×C₈	semidirect
177. Q₈×C₁₀₇	C₂²×C₈	semidirect
183. D₄×C₁₀₇	C₂²×C₈	semidirect
215. C₈×C₁₀₇	C₂²×C₈	semidirect
216. C₈×C₁₀₇	AGL(1,ℤ/8)	direct (N × H)
240. C₈×AGL(1,ℤ/8)	C₁₀₇	direct (N × H)
247. C₈×#41	C₂×C₁₀₇	semidirect
249. C₂×C₈×D₄	C₂×C₁₀₇	semidirect
250. #1580	C₂×C₁₀₇	semidirect
251. SD₁₆⋊C₈	C₂×C₁₀₇	semidirect
252. C₈×SD₁₆	C₂×C₁₀₇	semidirect
253. C₈×D₈	C₂×C₁₀₇	semidirect
254. #1565	C₂×C₁₀₇	semidirect
255. #1478	C₂×C₁₀₇	semidirect
256. #1477	C₂×C₁₀₇	semidirect
257. C₈×M₁₆	C₂×C₁₀₇	semidirect
258. C₁₀₇	C₈×AGL(1,ℤ/8)	direct (N × H)
263. C₈×Q₈	C₂²×C₁₀₇	semidirect
264. C₈×Q₈	C₂²×C₁₀₇	semidirect
275. C₈×D₄	C₂²×C₁₀₇	semidirect
276. C₈×D₄	C₂²×C₁₀₇	semidirect
288. #335	C₂²×C₁₀₇	semidirect
289. #334	C₂²×C₁₀₇	semidirect
290. Q₈⋊C₈	C₂²×C₁₀₇	semidirect
293. D₄⋊C₈	C₂²×C₁₀₇	semidirect
294. #322	C₂²×C₁₀₇	semidirect
295. C₈²	C₂²×C₁₀₇	semidirect
299. AGL(1,ℤ/8)	C₈×C₁₀₇	direct (N × H)
359. #41	C₂×C₈×C₁₀₇	semidirect
364. C₂×D₄	C₂×C₈×C₁₀₇	semidirect
378. SD₁₆	C₂×C₈×C₁₀₇	semidirect
379. D₈	C₂×C₈×C₁₀₇	semidirect
381. M₁₆	C₂×C₈×C₁₀₇	semidirect
424. Q₈	C₂²×C₈×C₁₀₇	semidirect
430. D₄	C₂²×C₈×C₁₀₇	semidirect
462. C₈	C₂²×C₈×C₁₀₇	semidirect
463. C₈	AGL(1,ℤ/8)×C₁₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#41×C₁₀₇	2
C₄×AGL(1,ℤ/8)×C₁₀₇	2
C₂×C₈×D₄×C₁₀₇	2
C₁₀₇×#1580	2
C₁₀₇×SD₁₆⋊C₈	2
C₈×SD₁₆×C₁₀₇	2
C₈×D₈×C₁₀₇	2
C₁₀₇×#1565	2
C₁₀₇×#1478	2
C₁₀₇×#1477	2
C₈×M₁₆×C₁₀₇	2
C₈×AGL(1,ℤ/8)	107

Subgroups — C8×AGL(1,ℤ/8)×C107 #41043814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×AGL(1,ℤ/8)×C₁₀₇ #41043814