Subgroups — C₁₀₇×#18064 #41044028

Order 27392.

718 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×#2974	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇×#1594	C₂	1	2	yes	maximal, complemented
4	C₁₀₇×#1581	C₂	1	4	yes	maximal, complemented
5	C₁₀₇×#1580	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₇×#1490	C₂	1	2	yes	maximal, complemented
8	C₁₀₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₁₀₇	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₀₇	C₂²	1	2	yes	—
11	C₄×D₈×C₁₀₇	C₄	1	2	yes	—
12	C₄×D₈×C₁₀₇	C₄	1	1	yes	characteristic
13	C₄×D₈×C₁₀₇	C₄	1	1	yes	characteristic
14	C₄×D₈×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₄×D₈×C₁₀₇	C₂²	1	2	yes	—
16	C₄×D₈×C₁₀₇	C₂²	1	1	yes	characteristic
17	#436×C₁₀₇	C₂²	1	4	yes	complemented
18	#435×C₁₀₇	—	2	4	no	—
19	C₈×D₄×C₁₀₇	C₂²	1	4	yes	complemented
20	#432×C₁₀₇	C₂²	1	2	yes	—
21	#431×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×#107×C₁₀₇	C₄	1	1	yes	characteristic
23	C₂×#102×C₁₀₇	C₄	1	2	yes	—
24	#407×C₁₀₇	—	2	2	no	—
25	C₂×C₂²⋊C₈×C₁₀₇	—	2	2	no	—
26	C₄×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
28	#335×C₁₀₇	C₂²	1	2	yes	complemented
29	#334×C₁₀₇	C₂²	1	2	yes	complemented
30	D₄⋊C₈×C₁₀₇	C₂²	1	4	yes	complemented
31	D₄⋊C₈×C₁₀₇	C₂²	1	4	yes	complemented
32	#322×C₁₀₇	C₂²	1	2	yes	complemented
33	#322×C₁₀₇	C₂²	1	2	yes	complemented
34	C₂²×D₄×C₁₀₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₀₇	—	2	2	no	—
36	C₂×D₈×C₁₀₇	—	2	4	no	—
37	C₂×D₈×C₁₀₇	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
39	C₂×D₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₁₀₇	—	2	1	no	—
41	C₂×M₁₆×C₁₀₇	—	2	4	no	—
42	C₂²×C₈×C₁₀₇	—	2	4	no	—
43	C₂²×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
45	C₄×D₄×C₁₀₇	—	2	2	no	—
46	C₄×D₄×C₁₀₇	—	2	2	no	—
47	C₄×D₄×C₁₀₇	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₁₀₇	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₁₀₇	C₂³	1	2	yes	—
50	C₄×D₄×C₁₀₇	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
53	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
54	#107×C₁₀₇	C₂×C₄	1	2	yes	—
55	#107×C₁₀₇	C₂×C₄	1	1	yes	characteristic
56	#107×C₁₀₇	C₂×C₄	1	1	yes	characteristic
57	C₄⋊C₈×C₁₀₇	D₄	1	2	yes	—
58	C₄⋊C₈×C₁₀₇	C₂³	1	4	yes	—
59	#102×C₁₀₇	C₂×C₄	1	2	yes	—
60	#102×C₁₀₇	C₂×C₄	1	2	yes	—
61	#102×C₁₀₇	C₂×C₄	1	2	yes	—
62	#102×C₁₀₇	C₂×C₄	1	2	yes	—
63	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
64	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
65	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
66	C₂²⋊C₈×C₁₀₇	D₄	1	2	yes	—
67	#97×C₁₀₇	—	2	2	no	—
68	#97×C₁₀₇	—	2	1	no	—
69	C₄×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
72	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
75	C₂⁴×C₁₀₇	—	2	2	no	—
76	C₂×D₄×C₁₀₇	—	2	4	no	—
77	C₂×D₄×C₁₀₇	—	2	2	no	—
78	C₂×D₄×C₁₀₇	—	4	2	no	—
79	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
80	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₀₇	—	2	2	no	—
82	C₂²×C₄×C₁₀₇	—	2	2	no	—
83	C₂²×C₄×C₁₀₇	—	2	2	no	—
84	C₂²×C₄×C₁₀₇	—	2	2	no	—
85	C₂²×C₄×C₁₀₇	—	2	2	no	—
86	C₂²×C₄×C₁₀₇	—	8	4	no	—
87	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
90	D₈×C₁₀₇	—	2	4	no	—
91	D₈×C₁₀₇	—	2	2	no	—
92	D₈×C₁₀₇	M₁₆	1	4	yes	complemented
93	M₁₆×C₁₀₇	—	4	2	no	—
94	M₁₆×C₁₀₇	—	8	4	no	—
95	C₂×C₈×C₁₀₇	—	2	2	no	—
96	C₂×C₈×C₁₀₇	—	2	4	no	—
97	C₂×C₈×C₁₀₇	—	2	2	no	—
98	C₂×C₈×C₁₀₇	—	4	1	no	—
99	C₂×C₈×C₁₀₇	—	8	4	no	—
100	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₀₇	C₂×D₄	1	4	yes	—
105	C₄⋊C₄×C₁₀₇	—	2	2	no	—
106	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
107	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
108	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
109	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
110	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
111	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
112	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₀₇	#41	1	1	yes	characteristic
115	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
116	C₂³×C₁₀₇	—	2	2	no	—
117	C₂³×C₁₀₇	—	2	2	no	—
118	C₂³×C₁₀₇	—	4	4	no	—
119	C₂³×C₁₀₇	—	4	4	no	—
120	C₂³×C₁₀₇	—	8	2	no	—
121	C₂³×C₁₀₇	C₄×D₄	1	1	yes	characteristic
122	D₄×C₁₀₇	—	2	2	no	—
123	D₄×C₁₀₇	—	2	2	no	—
124	D₄×C₁₀₇	—	2	2	no	—
125	D₄×C₁₀₇	—	4	4	no	—
126	D₄×C₁₀₇	C₂×M₁₆	1	4	yes	—
127	C₂×C₄×C₁₀₇	—	2	2	no	—
128	C₂×C₄×C₁₀₇	—	2	1	no	—
129	C₂×C₄×C₁₀₇	—	2	1	no	—
130	C₂×C₄×C₁₀₇	—	2	2	no	—
131	C₂×C₄×C₁₀₇	—	2	2	no	—
132	C₂×C₄×C₁₀₇	—	2	2	no	—
133	C₂×C₄×C₁₀₇	—	4	4	no	—
134	C₂×C₄×C₁₀₇	—	4	4	no	—
135	C₂×C₄×C₁₀₇	—	8	2	no	—
136	C₂×C₄×C₁₀₇	—	8	2	no	—
137	C₂×C₄×C₁₀₇	—	8	2	no	—
138	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
144	C₈×C₁₀₇	—	2	1	no	—
145	C₈×C₁₀₇	—	2	1	no	—
146	C₈×C₁₀₇	—	2	1	no	—
147	C₈×C₁₀₇	—	2	4	no	—
148	C₈×C₁₀₇	—	4	2	no	—
149	C₈×C₁₀₇	—	4	4	no	—
150	C₈×C₁₀₇	C₂×M₁₆	1	2	yes	—
151	C₂²×C₁₀₇	—	2	1	no	—
152	C₂²×C₁₀₇	—	2	1	no	—
153	C₂²×C₁₀₇	—	2	4	no	—
154	C₂²×C₁₀₇	—	4	2	no	—
155	C₂²×C₁₀₇	—	4	2	no	—
156	C₂²×C₁₀₇	—	4	2	no	—
157	C₂²×C₁₀₇	—	4	2	no	—
158	C₂²×C₁₀₇	—	4	2	no	—
159	C₂²×C₁₀₇	—	8	8	no	—
160	C₂²×C₁₀₇	#444	1	2	yes	—
161	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
162	C₄×C₁₀₇	—	2	1	no	—
163	C₄×C₁₀₇	—	2	1	no	—
164	C₄×C₁₀₇	—	2	1	no	—
165	C₄×C₁₀₇	—	2	1	no	—
166	C₄×C₁₀₇	—	4	2	no	—
167	C₄×C₁₀₇	—	4	2	no	—
168	C₄×C₁₀₇	C₂²×M₁₆	1	1	yes	characteristic
169	C₄×C₁₀₇	#568	1	1	yes	characteristic
170	C₄×C₁₀₇	#576	1	2	yes	—
171	#18064	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂×C₁₀₇	—	2	2	no	—
173	C₂×C₁₀₇	—	4	4	no	—
174	C₂×C₁₀₇	—	8	2	no	—
175	C₂×C₁₀₇	D₄×M₁₆	1	1	yes	characteristic
176	C₂×C₁₀₇	#2948	1	1	yes	characteristic
177	C₂×C₁₀₇	C₂×#444	1	1	yes	characteristic
178	#2974	C₂×C₁₀₇	1	2	yes	complemented
179	C₂×C₄×D₈	C₂×C₁₀₇	1	1	yes	characteristic
180	#1594	C₂×C₁₀₇	1	2	yes	complemented
181	#1581	C₂×C₁₀₇	1	4	yes	complemented
182	#1580	C₂×C₁₀₇	1	2	yes	complemented
183	#1568	C₂×C₁₀₇	1	1	yes	characteristic, complemented
184	#1490	C₂×C₁₀₇	1	2	yes	complemented
185	#1451	C₂×C₁₀₇	1	1	yes	characteristic, complemented
186	C₁₀₇	#18064	1	1	yes	characteristic, direct product factor, Sylow
187	C₂²×D₈	C₄×C₁₀₇	1	1	yes	characteristic
188	C₂×C₄×D₄	C₂²×C₁₀₇	1	2	yes	—
189	C₄×D₈	C₄×C₁₀₇	1	2	yes	—
190	C₄×D₈	C₄×C₁₀₇	1	1	yes	characteristic
191	C₄×D₈	C₄×C₁₀₇	1	1	yes	characteristic
192	C₄×D₈	C₂²×C₁₀₇	1	1	yes	characteristic
193	C₄×D₈	C₂²×C₁₀₇	1	2	yes	—
194	C₄×D₈	C₂²×C₁₀₇	1	1	yes	characteristic
195	#436	C₂²×C₁₀₇	1	4	yes	complemented
196	#435	—	2	4	no	—
197	C₈×D₄	C₂²×C₁₀₇	1	4	yes	complemented
198	#432	C₂²×C₁₀₇	1	2	yes	—
199	#431	C₂²×C₁₀₇	1	1	yes	characteristic
200	C₂×#107	C₄×C₁₀₇	1	1	yes	characteristic
201	C₂×#102	C₄×C₁₀₇	1	2	yes	—
202	#407	—	2	2	no	—
203	C₂×C₂²⋊C₈	—	2	2	no	—
204	C₄×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
206	#335	C₂²×C₁₀₇	1	2	yes	complemented
207	#334	C₂²×C₁₀₇	1	2	yes	complemented
208	D₄⋊C₈	C₂²×C₁₀₇	1	4	yes	complemented
209	D₄⋊C₈	C₂²×C₁₀₇	1	4	yes	complemented
210	#322	C₂²×C₁₀₇	1	2	yes	complemented
211	#322	C₂²×C₁₀₇	1	2	yes	complemented
212	C₂²×D₄	C₂×C₄×C₁₀₇	1	2	yes	—
213	C₂³×C₄	—	2	2	no	—
214	C₂×D₈	—	2	4	no	—
215	C₂×D₈	C₂×C₄×C₁₀₇	1	2	yes	—
216	C₂×D₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
217	C₂×D₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
218	C₂×M₁₆	—	2	1	no	—
219	C₂×M₁₆	—	2	4	no	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	C₂×C₄×C₁₀₇	1	2	yes	—
226	C₄×D₄	C₂×C₄×C₁₀₇	1	2	yes	—
227	C₄×D₄	C₂³×C₁₀₇	1	2	yes	—
228	C₄×D₄	C₂³×C₁₀₇	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
232	#107	C₂×C₄×C₁₀₇	1	2	yes	—
233	#107	C₂×C₄×C₁₀₇	1	1	yes	characteristic
234	#107	C₂×C₄×C₁₀₇	1	1	yes	characteristic
235	C₄⋊C₈	D₄×C₁₀₇	1	2	yes	—
236	C₄⋊C₈	C₂³×C₁₀₇	1	4	yes	—
237	#102	C₂×C₄×C₁₀₇	1	2	yes	—
238	#102	C₂×C₄×C₁₀₇	1	2	yes	—
239	#102	C₂×C₄×C₁₀₇	1	2	yes	—
240	#102	C₂×C₄×C₁₀₇	1	2	yes	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	2	4	no	—
243	C₂²⋊C₈	—	2	4	no	—
244	C₂²⋊C₈	D₄×C₁₀₇	1	2	yes	—
245	#97	—	2	2	no	—
246	#97	—	2	1	no	—
247	C₄×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
248	C₄×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
249	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
250	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
251	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
252	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
253	C₂⁴	—	2	2	no	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	—	4	2	no	—
257	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
258	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	8	4	no	—
265	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
267	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
268	D₈	—	2	4	no	—
269	D₈	—	2	2	no	—
270	D₈	M₁₆×C₁₀₇	1	4	yes	complemented
271	M₁₆	—	4	2	no	—
272	M₁₆	—	8	4	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	4	1	no	—
277	C₂×C₈	—	8	4	no	—
278	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
279	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
280	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
281	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
282	C₂×C₈	C₂×D₄×C₁₀₇	1	4	yes	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
285	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
286	C₂²⋊C₄	—	2	2	no	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₂²⋊C₄	—	2	2	no	—
290	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
291	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
292	C₄²	#41×C₁₀₇	1	1	yes	characteristic
293	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	4	4	no	—
298	C₂³	—	8	2	no	—
299	C₂³	C₄×D₄×C₁₀₇	1	1	yes	characteristic
300	D₄	—	2	2	no	—
301	D₄	—	2	2	no	—
302	D₄	—	2	2	no	—
303	D₄	—	4	4	no	—
304	D₄	C₂×M₁₆×C₁₀₇	1	4	yes	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	8	2	no	—
314	C₂×C₄	—	8	2	no	—
315	C₂×C₄	—	8	2	no	—
316	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
317	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
318	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
319	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
320	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
321	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
322	C₈	—	2	1	no	—
323	C₈	—	2	1	no	—
324	C₈	—	2	1	no	—
325	C₈	—	2	4	no	—
326	C₈	—	4	2	no	—
327	C₈	—	4	4	no	—
328	C₈	C₂×M₁₆×C₁₀₇	1	2	yes	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	8	8	no	—
338	C₂²	#444×C₁₀₇	1	2	yes	—
339	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	4	2	no	—
345	C₄	—	4	2	no	—
346	C₄	C₂²×M₁₆×C₁₀₇	1	1	yes	characteristic
347	C₄	#568×C₁₀₇	1	1	yes	characteristic
348	C₄	#576×C₁₀₇	1	2	yes	—
349	C₂	—	2	2	no	—
350	C₂	—	4	4	no	—
351	C₂	—	8	2	no	—
352	C₂	D₄×M₁₆×C₁₀₇	1	1	yes	characteristic
353	C₂	C₁₀₇×#2948	1	1	yes	characteristic
354	C₂	C₂×#444×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₇
Frattini, cosocle	C₄²	C₂⁴×C₁₀₇
socle	C₂²×C₁₀₇	C₂×C₄×D₄
prime radical	C₂²×D₈×C₁₀₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₇ ◁ #431×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₇×#2974	C₂	semidirect
3. C₁₀₇×#1594	C₂	semidirect
4. C₁₀₇×#1581	C₂	semidirect
5. C₁₀₇×#1580	C₂	semidirect
6. C₁₀₇×#1568	C₂	semidirect
7. C₁₀₇×#1490	C₂	semidirect
8. C₁₀₇×#1451	C₂	semidirect
17. #436×C₁₀₇	C₂²	semidirect
19. C₈×D₄×C₁₀₇	C₂²	semidirect
28. #335×C₁₀₇	C₂²	semidirect
29. #334×C₁₀₇	C₂²	semidirect
30. D₄⋊C₈×C₁₀₇	C₂²	semidirect
31. D₄⋊C₈×C₁₀₇	C₂²	semidirect
32. #322×C₁₀₇	C₂²	semidirect
33. #322×C₁₀₇	C₂²	semidirect
92. D₈×C₁₀₇	M₁₆	semidirect
171. #18064	C₁₀₇	direct (N × H)
178. #2974	C₂×C₁₀₇	semidirect
180. #1594	C₂×C₁₀₇	semidirect
181. #1581	C₂×C₁₀₇	semidirect
182. #1580	C₂×C₁₀₇	semidirect
183. #1568	C₂×C₁₀₇	semidirect
184. #1490	C₂×C₁₀₇	semidirect
185. #1451	C₂×C₁₀₇	semidirect
186. C₁₀₇	#18064	direct (N × H)
195. #436	C₂²×C₁₀₇	semidirect
197. C₈×D₄	C₂²×C₁₀₇	semidirect
206. #335	C₂²×C₁₀₇	semidirect
207. #334	C₂²×C₁₀₇	semidirect
208. D₄⋊C₈	C₂²×C₁₀₇	semidirect
209. D₄⋊C₈	C₂²×C₁₀₇	semidirect
210. #322	C₂²×C₁₀₇	semidirect
211. #322	C₂²×C₁₀₇	semidirect
270. D₈	M₁₆×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×#2974	2
C₂×C₄×D₈×C₁₀₇	2
C₁₀₇×#1594	2
C₁₀₇×#1581	2
C₁₀₇×#1580	2
C₁₀₇×#1568	2
C₁₀₇×#1490	2
C₁₀₇×#1451	2
#18064	107

Subgroups — C107×#18064 #41044028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#18064 #41044028