Subgroups — C₁₀₇×#23067 #41049031

Order 27392.

814 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#476×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇×#2369	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₇×#2354	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₇×#1936	C₂	1	2	yes	maximal
7	C₁₀₇×#1925	C₂	1	2	yes	maximal
8	C₁₀₇×#1919	C₂	1	2	yes	maximal, complemented
9	C₁₀₇×#1776	C₂	1	2	yes	maximal, complemented
10	C₁₀₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₁₀₇	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₀₇	—	2	1	no	—
15	#476×C₁₀₇	C₄	1	8	yes	complemented
16	C₂×#107×C₁₀₇	C₂²	1	2	yes	—
17	C₂×#106×C₁₀₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
19	C₂×#102×C₁₀₇	C₂²	1	1	yes	characteristic
20	C₂×#102×C₁₀₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₁₀₇	C₂²	1	2	yes	—
22	C₂×#97×C₁₀₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
24	#391×C₁₀₇	—	2	2	no	—
25	#390×C₁₀₇	C₂²	1	2	yes	—
26	#389×C₁₀₇	—	2	1	no	—
27	#389×C₁₀₇	C₂²	1	2	yes	—
28	#388×C₁₀₇	—	2	2	no	—
29	#384×C₁₀₇	C₂²	1	1	yes	characteristic
30	#380×C₁₀₇	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₀₇	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
36	#340×C₁₀₇	C₂²	1	1	yes	characteristic
37	#340×C₁₀₇	C₂²	1	2	yes	—
38	#340×C₁₀₇	C₂²	1	2	yes	—
39	#340×C₁₀₇	C₂²	1	2	yes	—
40	#340×C₁₀₇	C₂²	1	1	yes	characteristic
41	#336×C₁₀₇	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₀₇	—	2	1	no	—
43	C₂²×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₀₇	—	2	1	no	—
45	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
48	C₄⋊Q₈×C₁₀₇	—	2	2	no	—
49	C₄⋊Q₈×C₁₀₇	C₂×C₄	1	4	yes	—
50	C₄×D₄×C₁₀₇	—	2	2	no	—
51	C₄×D₄×C₁₀₇	C₂×C₄	1	4	yes	—
52	#117×C₁₀₇	—	4	4	no	—
53	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
67	C₂×C₄²×C₁₀₇	—	2	1	no	—
68	C₂×C₄²×C₁₀₇	—	2	2	no	—
69	C₂×C₄²×C₁₀₇	—	2	2	no	—
70	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
72	#107×C₁₀₇	—	2	4	no	—
73	#106×C₁₀₇	C₂×C₄	1	8	yes	—
74	C₄⋊C₈×C₁₀₇	C₂×C₄	1	4	yes	—
75	#102×C₁₀₇	—	2	2	no	—
76	#102×C₁₀₇	—	2	2	no	—
77	#102×C₁₀₇	C₂×C₄	1	8	yes	—
78	#97×C₁₀₇	—	2	4	no	—
79	C₄×C₈×C₁₀₇	—	2	2	no	—
80	#95×C₁₀₇	—	2	2	no	—
81	#95×C₁₀₇	—	2	2	no	—
82	#95×C₁₀₇	—	2	2	no	—
83	#95×C₁₀₇	—	2	1	no	—
84	#95×C₁₀₇	D₄	1	2	yes	—
85	C₂⁴×C₁₀₇	—	2	1	no	—
86	C₂×Q₈×C₁₀₇	—	2	4	no	—
87	C₂×Q₈×C₁₀₇	—	8	1	no	—
88	C₂×Q₈×C₁₀₇	—	8	1	no	—
89	C₂×D₄×C₁₀₇	—	2	1	no	—
90	C₂×D₄×C₁₀₇	—	2	1	no	—
91	C₂×D₄×C₁₀₇	—	2	1	no	—
92	C₂×D₄×C₁₀₇	—	2	1	no	—
93	C₂×D₄×C₁₀₇	—	2	1	no	—
94	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₀₇	—	2	1	no	—
96	C₂²×C₄×C₁₀₇	—	2	1	no	—
97	C₂²×C₄×C₁₀₇	—	2	2	no	—
98	C₂²×C₄×C₁₀₇	—	2	4	no	—
99	C₂²×C₄×C₁₀₇	—	2	1	no	—
100	C₂²×C₄×C₁₀₇	—	2	2	no	—
101	C₂²×C₄×C₁₀₇	—	4	2	no	—
102	C₂²×C₄×C₁₀₇	—	4	2	no	—
103	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₀₇	—	2	1	no	—
109	C₂×C₈×C₁₀₇	—	2	2	no	—
110	C₂×C₈×C₁₀₇	—	2	2	no	—
111	C₂×C₈×C₁₀₇	—	2	1	no	—
112	C₂×C₈×C₁₀₇	—	2	1	no	—
113	C₂×C₈×C₁₀₇	—	2	1	no	—
114	C₂×C₈×C₁₀₇	—	2	1	no	—
115	C₂×C₈×C₁₀₇	C₂²×C₄	1	4	yes	—
116	C₂×C₈×C₁₀₇	#41	1	2	yes	—
117	C₄⋊C₄×C₁₀₇	—	2	4	no	—
118	C₄⋊C₄×C₁₀₇	—	2	2	no	—
119	C₄⋊C₄×C₁₀₇	—	2	2	no	—
120	C₄⋊C₄×C₁₀₇	—	2	1	no	—
121	C₄⋊C₄×C₁₀₇	—	2	2	no	—
122	C₄⋊C₄×C₁₀₇	—	2	1	no	—
123	C₄⋊C₄×C₁₀₇	—	2	1	no	—
124	C₄⋊C₄×C₁₀₇	—	2	2	no	—
125	C₄⋊C₄×C₁₀₇	—	2	1	no	—
126	C₄⋊C₄×C₁₀₇	—	2	2	no	—
127	C₄⋊C₄×C₁₀₇	—	4	2	no	—
128	C₄⋊C₄×C₁₀₇	—	8	1	no	—
129	C₄⋊C₄×C₁₀₇	—	8	2	no	—
130	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
131	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
132	C₄⋊C₄×C₁₀₇	#41	1	2	yes	—
133	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
134	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
135	C₂²⋊C₄×C₁₀₇	—	8	2	no	—
136	C₄²×C₁₀₇	—	2	2	no	—
137	C₄²×C₁₀₇	—	2	2	no	—
138	C₄²×C₁₀₇	—	4	4	no	—
139	C₄²×C₁₀₇	—	4	2	no	—
140	C₄²×C₁₀₇	—	8	2	no	—
141	C₄²×C₁₀₇	C₂²×C₄	1	2	yes	—
142	C₄²×C₁₀₇	#41	1	2	yes	—
143	C₂³×C₁₀₇	—	2	2	no	—
144	C₂³×C₁₀₇	—	4	1	no	—
145	C₂³×C₁₀₇	—	4	1	no	—
146	C₂³×C₁₀₇	—	4	1	no	—
147	C₂³×C₁₀₇	—	4	1	no	—
148	C₂³×C₁₀₇	—	4	1	no	—
149	C₂³×C₁₀₇	—	4	1	no	—
150	C₂³×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₀₇	—	8	4	no	—
152	D₄×C₁₀₇	—	2	2	no	—
153	D₄×C₁₀₇	—	2	2	no	—
154	D₄×C₁₀₇	—	4	1	no	—
155	D₄×C₁₀₇	—	4	1	no	—
156	C₂×C₄×C₁₀₇	—	2	1	no	—
157	C₂×C₄×C₁₀₇	—	2	1	no	—
158	C₂×C₄×C₁₀₇	—	2	2	no	—
159	C₂×C₄×C₁₀₇	—	2	4	no	—
160	C₂×C₄×C₁₀₇	—	2	2	no	—
161	C₂×C₄×C₁₀₇	—	2	2	no	—
162	C₂×C₄×C₁₀₇	—	2	2	no	—
163	C₂×C₄×C₁₀₇	—	2	2	no	—
164	C₂×C₄×C₁₀₇	—	2	2	no	—
165	C₂×C₄×C₁₀₇	—	2	2	no	—
166	C₂×C₄×C₁₀₇	—	2	2	no	—
167	C₂×C₄×C₁₀₇	—	4	1	no	—
168	C₂×C₄×C₁₀₇	—	4	1	no	—
169	C₂×C₄×C₁₀₇	—	4	1	no	—
170	C₂×C₄×C₁₀₇	—	4	1	no	—
171	C₂×C₄×C₁₀₇	—	4	2	no	—
172	C₂×C₄×C₁₀₇	—	4	2	no	—
173	C₂×C₄×C₁₀₇	—	4	8	no	—
174	C₂×C₄×C₁₀₇	—	4	1	no	—
175	C₂×C₄×C₁₀₇	—	4	2	no	—
176	C₂×C₄×C₁₀₇	—	4	2	no	—
177	C₂×C₄×C₁₀₇	—	4	1	no	—
178	C₂×C₄×C₁₀₇	—	4	2	no	—
179	C₂×C₄×C₁₀₇	—	4	1	no	—
180	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
183	C₂×C₄×C₁₀₇	#137	1	2	yes	—
184	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₀₇	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₄×C₁₀₇	2₋¹⁺⁴	1	1	yes	characteristic
190	C₈×C₁₀₇	—	2	4	no	—
191	C₈×C₁₀₇	—	2	2	no	—
192	C₈×C₁₀₇	—	4	1	no	—
193	C₂²×C₁₀₇	—	4	2	no	—
194	C₂²×C₁₀₇	—	4	2	no	—
195	C₂²×C₁₀₇	—	4	2	no	—
196	C₂²×C₁₀₇	—	8	1	no	—
197	C₂²×C₁₀₇	—	8	1	no	—
198	C₂²×C₁₀₇	—	8	1	no	—
199	C₂²×C₁₀₇	—	8	1	no	—
200	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂²×C₁₀₇	#547	1	1	yes	characteristic
202	C₂²×C₁₀₇	#548	1	1	yes	characteristic
203	C₂²×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₂²×C₁₀₇	C₂×#137	1	1	yes	characteristic
205	C₂²×C₁₀₇	#576	1	1	yes	characteristic
206	C₂²×C₁₀₇	#577	1	1	yes	characteristic
207	C₄×C₁₀₇	—	2	2	no	—
208	C₄×C₁₀₇	—	4	2	no	—
209	C₄×C₁₀₇	—	4	2	no	—
210	C₄×C₁₀₇	—	4	2	no	—
211	C₄×C₁₀₇	—	4	2	no	—
212	C₄×C₁₀₇	—	4	4	no	—
213	C₄×C₁₀₇	—	8	1	no	—
214	C₄×C₁₀₇	—	8	2	no	—
215	C₄×C₁₀₇	#440	1	4	yes	—
216	C₄×C₁₀₇	C₄×#41	1	1	yes	characteristic
217	C₄×C₁₀₇	#519	1	1	yes	characteristic
218	C₄×C₁₀₇	#552	1	1	yes	characteristic
219	C₄×C₁₀₇	#556	1	1	yes	characteristic
220	#23067	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂×C₁₀₇	—	8	2	no	—
222	C₂×C₁₀₇	#2362	1	1	yes	characteristic
223	C₂×C₁₀₇	C₂×#440	1	1	yes	characteristic
224	C₂×C₁₀₇	#2946	1	1	yes	characteristic
225	C₂×C₁₀₇	#3354	1	1	yes	characteristic
226	C₂×C₁₀₇	#3357	1	1	yes	characteristic
227	C₂×C₁₀₇	#3366	1	1	yes	characteristic
228	C₂×C₁₀₇	#3369	1	1	yes	characteristic
229	C₂×#476	C₂×C₁₀₇	1	1	yes	characteristic
230	#2369	C₂×C₁₀₇	1	1	yes	characteristic, complemented
231	#2354	C₂×C₁₀₇	1	1	yes	characteristic
232	#1990	C₂×C₁₀₇	1	1	yes	characteristic, complemented
233	#1947	C₂×C₁₀₇	1	1	yes	characteristic, complemented
234	#1936	C₂×C₁₀₇	1	2	yes	—
235	#1925	C₂×C₁₀₇	1	2	yes	—
236	#1919	C₂×C₁₀₇	1	2	yes	complemented
237	#1776	C₂×C₁₀₇	1	2	yes	complemented
238	#1770	C₂×C₁₀₇	1	1	yes	characteristic, complemented
239	C₄×#102	C₂×C₁₀₇	1	1	yes	characteristic
240	C₁₀₇	#23067	1	1	yes	characteristic, direct product factor, Sylow
241	C₂×C₄⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
243	C₂×#117	—	2	1	no	—
244	#476	C₄×C₁₀₇	1	8	yes	complemented
245	C₂×#107	C₂²×C₁₀₇	1	2	yes	—
246	C₂×#106	C₂²×C₁₀₇	1	2	yes	—
247	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
248	C₂×#102	C₂²×C₁₀₇	1	1	yes	characteristic
249	C₂×#102	C₂²×C₁₀₇	1	1	yes	characteristic
250	C₂×#102	C₂²×C₁₀₇	1	2	yes	—
251	C₂×#97	C₂²×C₁₀₇	1	2	yes	—
252	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
253	#391	—	2	2	no	—
254	#390	C₂²×C₁₀₇	1	2	yes	—
255	#389	—	2	1	no	—
256	#389	C₂²×C₁₀₇	1	2	yes	—
257	#388	—	2	2	no	—
258	#384	C₂²×C₁₀₇	1	1	yes	characteristic
259	#380	—	2	1	no	—
260	C₄×C₄⋊C₄	—	2	1	no	—
261	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
262	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
263	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
264	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
265	#340	C₂²×C₁₀₇	1	1	yes	characteristic
266	#340	C₂²×C₁₀₇	1	2	yes	—
267	#340	C₂²×C₁₀₇	1	2	yes	—
268	#340	C₂²×C₁₀₇	1	2	yes	—
269	#340	C₂²×C₁₀₇	1	1	yes	characteristic
270	#336	C₂²×C₁₀₇	1	2	yes	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×D₄	C₂³×C₁₀₇	1	1	yes	characteristic
273	C₂³×C₄	—	2	1	no	—
274	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
276	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	C₂×C₄×C₁₀₇	1	4	yes	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	C₂×C₄×C₁₀₇	1	4	yes	—
281	#117	—	4	4	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
287	C₂×C₄⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
300	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
301	#107	—	2	4	no	—
302	#106	C₂×C₄×C₁₀₇	1	8	yes	—
303	C₄⋊C₈	C₂×C₄×C₁₀₇	1	4	yes	—
304	#102	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	C₂×C₄×C₁₀₇	1	8	yes	—
307	#97	—	2	4	no	—
308	C₄×C₈	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	D₄×C₁₀₇	1	2	yes	—
314	C₂⁴	—	2	1	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	8	1	no	—
317	C₂×Q₈	—	8	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	C₂²×C₄×C₁₀₇	1	4	yes	—
345	C₂×C₈	#41×C₁₀₇	1	2	yes	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	8	1	no	—
358	C₄⋊C₄	—	8	2	no	—
359	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
360	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
361	C₄⋊C₄	#41×C₁₀₇	1	2	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	4	4	no	—
364	C₂²⋊C₄	—	8	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	4	4	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	8	2	no	—
370	C₄²	C₂²×C₄×C₁₀₇	1	2	yes	—
371	C₄²	#41×C₁₀₇	1	2	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
380	Q₈	—	8	4	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
410	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
411	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
412	C₂×C₄	#137×C₁₀₇	1	2	yes	—
413	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
417	C₂×C₄	2₋¹⁺⁴×C₁₀₇	1	1	yes	characteristic
418	C₂×C₄	2₋¹⁺⁴×C₁₀₇	1	1	yes	characteristic
419	C₈	—	2	4	no	—
420	C₈	—	2	2	no	—
421	C₈	—	4	1	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
430	C₂²	#547×C₁₀₇	1	1	yes	characteristic
431	C₂²	#548×C₁₀₇	1	1	yes	characteristic
432	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
433	C₂²	C₂×#137×C₁₀₇	1	1	yes	characteristic
434	C₂²	#576×C₁₀₇	1	1	yes	characteristic
435	C₂²	#577×C₁₀₇	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	2	no	—
444	C₄	#440×C₁₀₇	1	4	yes	—
445	C₄	C₄×#41×C₁₀₇	1	1	yes	characteristic
446	C₄	#519×C₁₀₇	1	1	yes	characteristic
447	C₄	#552×C₁₀₇	1	1	yes	characteristic
448	C₄	#556×C₁₀₇	1	1	yes	characteristic
449	C₂	—	8	2	no	—
450	C₂	C₁₀₇×#2362	1	1	yes	characteristic
451	C₂	C₂×#440×C₁₀₇	1	1	yes	characteristic
452	C₂	C₁₀₇×#2946	1	1	yes	characteristic
453	C₂	C₁₀₇×#3354	1	1	yes	characteristic
454	C₂	C₁₀₇×#3357	1	1	yes	characteristic
455	C₂	C₁₀₇×#3366	1	1	yes	characteristic
456	C₂	C₁₀₇×#3369	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₀₇×#2369	C₂	semidirect
4. C₁₀₇×#1990	C₂	semidirect
5. C₁₀₇×#1947	C₂	semidirect
8. C₁₀₇×#1919	C₂	semidirect
9. C₁₀₇×#1776	C₂	semidirect
10. C₁₀₇×#1770	C₂	semidirect
15. #476×C₁₀₇	C₄	semidirect
220. #23067	C₁₀₇	direct (N × H)
230. #2369	C₂×C₁₀₇	semidirect
232. #1990	C₂×C₁₀₇	semidirect
233. #1947	C₂×C₁₀₇	semidirect
236. #1919	C₂×C₁₀₇	semidirect
237. #1776	C₂×C₁₀₇	semidirect
238. #1770	C₂×C₁₀₇	semidirect
240. C₁₀₇	#23067	direct (N × H)
244. #476	C₄×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#476×C₁₀₇	2
C₁₀₇×#2369	2
C₁₀₇×#2354	2
C₁₀₇×#1990	2
C₁₀₇×#1947	2
C₁₀₇×#1936	2
C₁₀₇×#1925	2
C₁₀₇×#1919	2
C₁₀₇×#1776	2
C₁₀₇×#1770	2
C₄×#102×C₁₀₇	2
#23067	107

Subgroups — C107×#23067 #41049031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#23067 #41049031