Subgroups — C₂×C₁₀₇×#1565 #41043750

Order 27392.

834 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#431×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1565	C₂	1	8	yes	maximal, direct product factor
5	C₂×#335×C₁₀₇	C₂	1	2	yes	maximal, complemented
6	C₂×#334×C₁₀₇	C₂	1	2	yes	maximal, complemented
7	C₂²×M₁₆×C₁₀₇	C₄	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₀₇	C₄	1	1	yes	characteristic
9	C₂³×C₈×C₁₀₇	—	2	1	no	—
10	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
11	#431×C₁₀₇	—	2	2	no	—
12	#431×C₁₀₇	C₂²	1	4	yes	—
13	C₂×C₄⋊C₈×C₁₀₇	—	2	2	no	—
14	C₂×C₄⋊C₈×C₁₀₇	—	2	1	no	—
15	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	4	yes	—
17	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₈×C₁₀₇	—	2	1	no	—
20	C₄×M₁₆×C₁₀₇	C₄	1	4	yes	—
21	C₄×M₁₆×C₁₀₇	C₂²	1	4	yes	—
22	C₂×#97×C₁₀₇	C₄	1	2	yes	—
23	C₂×C₄×C₈×C₁₀₇	—	2	1	no	—
24	C₂×C₄×C₈×C₁₀₇	C₂²	1	2	yes	—
25	#335×C₁₀₇	C₂²	1	8	yes	complemented
26	#334×C₁₀₇	C₂²	1	8	yes	complemented
27	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₀₇	Q₈	1	1	yes	characteristic
30	C₂×M₁₆×C₁₀₇	—	2	4	no	—
31	C₂×M₁₆×C₁₀₇	C₈	1	8	yes	complemented
32	C₂×M₁₆×C₁₀₇	C₂×C₄	1	4	yes	—
33	C₂×M₁₆×C₁₀₇	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₁₀₇	—	2	4	no	—
35	C₂²×C₈×C₁₀₇	—	2	1	no	—
36	C₂²×C₈×C₁₀₇	—	2	1	no	—
37	C₂²×C₈×C₁₀₇	—	2	2	no	—
38	C₂²×C₈×C₁₀₇	—	4	4	no	—
39	C₂²×C₈×C₁₀₇	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₁₀₇	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₀₇	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₁₀₇	D₄	1	2	yes	—
44	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₀₇	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₀₇	Q₈	1	2	yes	—
47	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
48	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
49	C₄⋊C₈×C₁₀₇	—	2	4	no	—
50	C₄⋊C₈×C₁₀₇	—	2	2	no	—
51	C₄⋊C₈×C₁₀₇	—	2	1	no	—
52	C₄⋊C₈×C₁₀₇	—	2	1	no	—
53	C₄⋊C₈×C₁₀₇	C₂³	1	4	yes	—
54	C₄⋊C₈×C₁₀₇	C₂³	1	2	yes	—
55	C₄⋊C₈×C₁₀₇	C₂³	1	2	yes	—
56	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
57	#97×C₁₀₇	C₂×C₄	1	8	yes	—
58	C₄×C₈×C₁₀₇	—	2	4	no	—
59	C₄×C₈×C₁₀₇	C₂×C₄	1	4	yes	—
60	C₄×C₈×C₁₀₇	C₂³	1	4	yes	—
61	C₂⁴×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₀₇	—	2	2	no	—
63	C₂²×C₄×C₁₀₇	—	2	2	no	—
64	C₂²×C₄×C₁₀₇	—	4	2	no	—
65	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₀₇	C₂×C₈	1	4	yes	—
72	C₂²×C₄×C₁₀₇	M₁₆	1	4	yes	—
73	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₇	C₂×Q₈	1	2	yes	—
79	M₁₆×C₁₀₇	—	2	8	no	—
80	M₁₆×C₁₀₇	C₂×C₈	1	16	yes	complemented
81	C₂×C₈×C₁₀₇	—	2	4	no	—
82	C₂×C₈×C₁₀₇	—	2	2	no	—
83	C₂×C₈×C₁₀₇	—	2	2	no	—
84	C₂×C₈×C₁₀₇	—	2	4	no	—
85	C₂×C₈×C₁₀₇	—	4	8	no	—
86	C₂×C₈×C₁₀₇	—	4	2	no	—
87	C₂×C₈×C₁₀₇	—	4	4	no	—
88	C₂×C₈×C₁₀₇	—	4	2	no	—
89	C₂×C₈×C₁₀₇	C₂×C₈	1	8	yes	complemented
90	C₂×C₈×C₁₀₇	C₂²×C₄	1	4	yes	—
91	C₂×C₈×C₁₀₇	C₂²×C₄	1	4	yes	—
92	C₄²×C₁₀₇	C₄⋊C₄	1	2	yes	—
93	C₄²×C₁₀₇	C₄⋊C₄	1	2	yes	—
94	C₄²×C₁₀₇	C₄⋊C₄	1	2	yes	—
95	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
96	C₄²×C₁₀₇	C₂²×C₄	1	2	yes	—
97	C₄²×C₁₀₇	C₂×D₄	1	2	yes	—
98	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₁₀₇	C₂×Q₈	1	2	yes	—
100	C₄²×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
101	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
102	C₂³×C₁₀₇	—	2	2	no	—
103	C₂³×C₁₀₇	—	2	2	no	—
104	C₂³×C₁₀₇	C₄⋊C₈	1	4	yes	—
105	C₂³×C₁₀₇	C₂×C₄⋊C₄	1	2	yes	—
106	C₂³×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₀₇	—	2	2	no	—
108	C₂×C₄×C₁₀₇	—	2	2	no	—
109	C₂×C₄×C₁₀₇	—	2	2	no	—
110	C₂×C₄×C₁₀₇	—	2	2	no	—
111	C₂×C₄×C₁₀₇	—	2	2	no	—
112	C₂×C₄×C₁₀₇	—	2	4	no	—
113	C₂×C₄×C₁₀₇	—	4	2	no	—
114	C₂×C₄×C₁₀₇	—	4	2	no	—
115	C₂×C₄×C₁₀₇	C₄⋊C₈	1	8	yes	—
116	C₂×C₄×C₁₀₇	C₄⋊C₈	1	4	yes	—
117	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	2	yes	—
119	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	2	yes	—
120	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	2	yes	—
121	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₀₇	C₂²×C₈	1	2	yes	—
124	C₂×C₄×C₁₀₇	C₂²×C₈	1	4	yes	—
125	C₂×C₄×C₁₀₇	C₂×M₁₆	1	2	yes	—
126	C₂×C₄×C₁₀₇	C₂×M₁₆	1	4	yes	—
127	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
128	C₂×C₄×C₁₀₇	#137	1	2	yes	—
129	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₀₇	C₂²×Q₈	1	1	yes	characteristic
132	C₈×C₁₀₇	—	2	4	no	—
133	C₈×C₁₀₇	—	4	2	no	—
134	C₈×C₁₀₇	—	4	4	no	—
135	C₈×C₁₀₇	—	4	2	no	—
136	C₈×C₁₀₇	C₂²×C₈	1	8	yes	complemented
137	C₂²×C₁₀₇	—	2	8	no	—
138	C₂²×C₁₀₇	—	2	2	no	—
139	C₂²×C₁₀₇	—	2	2	no	—
140	C₂²×C₁₀₇	C₂×C₄⋊C₈	1	4	yes	—
141	C₂²×C₁₀₇	C₂×C₄⋊C₈	1	2	yes	—
142	C₂²×C₁₀₇	#428	1	2	yes	—
143	C₂²×C₁₀₇	#430	1	2	yes	—
144	C₂²×C₁₀₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
145	C₄×C₁₀₇	—	2	2	no	—
146	C₄×C₁₀₇	—	2	2	no	—
147	C₄×C₁₀₇	—	2	1	no	—
148	C₄×C₁₀₇	—	2	1	no	—
149	C₄×C₁₀₇	C₂×C₄⋊C₈	1	2	yes	—
150	C₄×C₁₀₇	C₂×C₄⋊C₈	1	4	yes	—
151	C₄×C₁₀₇	#428	1	2	yes	—
152	C₄×C₁₀₇	C₂³×C₈	1	1	yes	characteristic
153	C₄×C₁₀₇	C₂²×M₁₆	1	1	yes	characteristic
154	C₄×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₄×C₁₀₇	C₂×#137	1	1	yes	characteristic
156	C₂×#1565	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂×C₁₀₇	—	2	4	no	—
158	C₂×C₁₀₇	#1565	1	4	yes	direct product factor
159	C₂×C₁₀₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
160	C₂×C₁₀₇	C₂×#428	1	1	yes	characteristic
161	C₂×C₁₀₇	C₂×#430	1	1	yes	characteristic
162	C₂×#431	C₂×C₁₀₇	1	1	yes	characteristic
163	C₂²×C₄⋊C₈	C₂×C₁₀₇	1	1	yes	characteristic
164	C₂×C₄×M₁₆	C₂×C₁₀₇	1	1	yes	characteristic
165	#1565	C₂×C₁₀₇	1	8	yes	direct product factor
166	C₂×#335	C₂×C₁₀₇	1	2	yes	complemented
167	C₂×#334	C₂×C₁₀₇	1	2	yes	complemented
168	C₁₀₇	C₂×#1565	1	1	yes	characteristic, direct product factor, Sylow
169	C₂²×M₁₆	C₄×C₁₀₇	1	1	yes	characteristic
170	C₂²×M₁₆	C₄×C₁₀₇	1	1	yes	characteristic
171	C₂³×C₈	—	2	1	no	—
172	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
173	#431	—	2	2	no	—
174	#431	C₂²×C₁₀₇	1	4	yes	—
175	C₂×C₄⋊C₈	—	2	1	no	—
176	C₂×C₄⋊C₈	—	2	2	no	—
177	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	2	yes	—
179	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
180	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	4	yes	—
181	C₂×C₂²⋊C₈	—	2	1	no	—
182	C₄×M₁₆	C₄×C₁₀₇	1	4	yes	—
183	C₄×M₁₆	C₂²×C₁₀₇	1	4	yes	—
184	C₂×#97	C₄×C₁₀₇	1	2	yes	—
185	C₂×C₄×C₈	—	2	1	no	—
186	C₂×C₄×C₈	C₂²×C₁₀₇	1	2	yes	—
187	#335	C₂²×C₁₀₇	1	8	yes	complemented
188	#334	C₂²×C₁₀₇	1	8	yes	complemented
189	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
190	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
191	C₂³×C₄	Q₈×C₁₀₇	1	1	yes	characteristic
192	C₂×M₁₆	—	2	4	no	—
193	C₂×M₁₆	C₈×C₁₀₇	1	8	yes	complemented
194	C₂×M₁₆	C₂×C₄×C₁₀₇	1	4	yes	—
195	C₂×M₁₆	C₂×C₄×C₁₀₇	1	4	yes	—
196	C₂²×C₈	—	2	4	no	—
197	C₂²×C₈	—	2	2	no	—
198	C₂²×C₈	—	2	1	no	—
199	C₂²×C₈	—	2	1	no	—
200	C₂²×C₈	—	4	4	no	—
201	C₂²×C₈	C₂×C₄×C₁₀₇	1	2	yes	—
202	C₂²×C₈	C₂×C₄×C₁₀₇	1	2	yes	—
203	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
204	C₂×C₄²	C₂×C₄×C₁₀₇	1	2	yes	—
205	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
206	C₂×C₄²	D₄×C₁₀₇	1	2	yes	—
207	C₂×C₄²	Q₈×C₁₀₇	1	1	yes	characteristic
208	C₂×C₄²	Q₈×C₁₀₇	1	2	yes	—
209	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
210	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
211	C₄⋊C₈	—	2	4	no	—
212	C₄⋊C₈	—	2	2	no	—
213	C₄⋊C₈	—	2	1	no	—
214	C₄⋊C₈	—	2	1	no	—
215	C₄⋊C₈	C₂³×C₁₀₇	1	2	yes	—
216	C₄⋊C₈	C₂³×C₁₀₇	1	4	yes	—
217	C₄⋊C₈	C₂³×C₁₀₇	1	2	yes	—
218	C₂²⋊C₈	—	2	4	no	—
219	#97	C₂×C₄×C₁₀₇	1	8	yes	—
220	C₄×C₈	—	2	4	no	—
221	C₄×C₈	C₂×C₄×C₁₀₇	1	4	yes	—
222	C₄×C₈	C₂³×C₁₀₇	1	4	yes	—
223	C₂⁴	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
228	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
229	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
230	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
231	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
232	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
233	C₂²×C₄	C₂×C₈×C₁₀₇	1	4	yes	—
234	C₂²×C₄	M₁₆×C₁₀₇	1	4	yes	—
235	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
237	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
238	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
239	C₂²×C₄	C₂×Q₈×C₁₀₇	1	1	yes	characteristic
240	C₂²×C₄	C₂×Q₈×C₁₀₇	1	2	yes	—
241	M₁₆	—	2	8	no	—
242	M₁₆	C₂×C₈×C₁₀₇	1	16	yes	complemented
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	—	4	8	no	—
248	C₂×C₈	—	4	4	no	—
249	C₂×C₈	—	4	2	no	—
250	C₂×C₈	—	4	2	no	—
251	C₂×C₈	C₂×C₈×C₁₀₇	1	8	yes	complemented
252	C₂×C₈	C₂²×C₄×C₁₀₇	1	4	yes	—
253	C₂×C₈	C₂²×C₄×C₁₀₇	1	4	yes	—
254	C₄²	C₄⋊C₄×C₁₀₇	1	2	yes	—
255	C₄²	C₄⋊C₄×C₁₀₇	1	2	yes	—
256	C₄²	C₄⋊C₄×C₁₀₇	1	2	yes	—
257	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
258	C₄²	C₂²×C₄×C₁₀₇	1	2	yes	—
259	C₄²	C₂×D₄×C₁₀₇	1	2	yes	—
260	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
261	C₄²	C₂×Q₈×C₁₀₇	1	2	yes	—
262	C₄²	C₂×Q₈×C₁₀₇	1	1	yes	characteristic
263	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
264	C₂³	—	2	2	no	—
265	C₂³	—	2	2	no	—
266	C₂³	C₄⋊C₈×C₁₀₇	1	4	yes	—
267	C₂³	C₂×C₄⋊C₄×C₁₀₇	1	2	yes	—
268	C₂³	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	C₄⋊C₈×C₁₀₇	1	8	yes	—
278	C₂×C₄	C₄⋊C₈×C₁₀₇	1	4	yes	—
279	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
280	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	2	yes	—
281	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	2	yes	—
282	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	2	yes	—
283	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
284	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
285	C₂×C₄	C₂²×C₈×C₁₀₇	1	2	yes	—
286	C₂×C₄	C₂²×C₈×C₁₀₇	1	4	yes	—
287	C₂×C₄	C₂×M₁₆×C₁₀₇	1	2	yes	—
288	C₂×C₄	C₂×M₁₆×C₁₀₇	1	4	yes	—
289	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
290	C₂×C₄	#137×C₁₀₇	1	2	yes	—
291	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
292	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
293	C₂×C₄	C₂²×Q₈×C₁₀₇	1	1	yes	characteristic
294	C₈	—	2	4	no	—
295	C₈	—	4	4	no	—
296	C₈	—	4	2	no	—
297	C₈	—	4	2	no	—
298	C₈	C₂²×C₈×C₁₀₇	1	8	yes	complemented
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	8	no	—
302	C₂²	C₂×C₄⋊C₈×C₁₀₇	1	4	yes	—
303	C₂²	C₂×C₄⋊C₈×C₁₀₇	1	2	yes	—
304	C₂²	#428×C₁₀₇	1	2	yes	—
305	C₂²	#430×C₁₀₇	1	2	yes	—
306	C₂²	C₂²×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
307	C₄	—	2	2	no	—
308	C₄	—	2	2	no	—
309	C₄	—	2	1	no	—
310	C₄	—	2	1	no	—
311	C₄	C₂×C₄⋊C₈×C₁₀₇	1	2	yes	—
312	C₄	C₂×C₄⋊C₈×C₁₀₇	1	4	yes	—
313	C₄	#428×C₁₀₇	1	2	yes	—
314	C₄	C₂³×C₈×C₁₀₇	1	1	yes	characteristic
315	C₄	C₂²×M₁₆×C₁₀₇	1	1	yes	characteristic
316	C₄	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
317	C₄	C₂×#137×C₁₀₇	1	1	yes	characteristic
318	C₂	—	2	4	no	—
319	C₂	C₁₀₇×#1565	1	4	yes	direct product factor
320	C₂	C₂²×C₄⋊C₈×C₁₀₇	1	1	yes	characteristic
321	C₂	C₂×#428×C₁₀₇	1	1	yes	characteristic
322	C₂	C₂×#430×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₇	C₂×D₄
commutator	C₄	C₂³×C₈×C₁₀₇
Frattini, cosocle	C₄²	C₂⁴×C₁₀₇
socle	C₂³×C₁₀₇	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₀₇	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₇ ◁ C₂²×C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₇×#1565	C₂	direct (N × H)
5. C₂×#335×C₁₀₇	C₂	semidirect
6. C₂×#334×C₁₀₇	C₂	semidirect
25. #335×C₁₀₇	C₂²	semidirect
26. #334×C₁₀₇	C₂²	semidirect
31. C₂×M₁₆×C₁₀₇	C₈	semidirect
80. M₁₆×C₁₀₇	C₂×C₈	semidirect
89. C₂×C₈×C₁₀₇	C₂×C₈	semidirect
136. C₈×C₁₀₇	C₂²×C₈	semidirect
156. C₂×#1565	C₁₀₇	direct (N × H)
158. C₂×C₁₀₇	#1565	direct (N × H)
165. #1565	C₂×C₁₀₇	direct (N × H)
166. C₂×#335	C₂×C₁₀₇	semidirect
167. C₂×#334	C₂×C₁₀₇	semidirect
168. C₁₀₇	C₂×#1565	direct (N × H)
187. #335	C₂²×C₁₀₇	semidirect
188. #334	C₂²×C₁₀₇	semidirect
193. C₂×M₁₆	C₈×C₁₀₇	semidirect
242. M₁₆	C₂×C₈×C₁₀₇	semidirect
251. C₂×C₈	C₂×C₈×C₁₀₇	semidirect
298. C₈	C₂²×C₈×C₁₀₇	semidirect
319. C₂	C₁₀₇×#1565	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×#431×C₁₀₇	2
C₂²×C₄⋊C₈×C₁₀₇	2
C₂×C₄×M₁₆×C₁₀₇	2
C₁₀₇×#1565	2
C₂×#335×C₁₀₇	2
C₂×#334×C₁₀₇	2
C₂×#1565	107

Subgroups — C2×C107×#1565 #41043750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#1565 #41043750