Subgroups — C₁₀₇×#21004 #41046968

Order 27392.

1686 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#568×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#417×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#413×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₇×#1908	C₂	1	4	yes	maximal, complemented
7	C₁₀₇×#1907	C₂	1	4	yes	maximal, complemented
8	C₂×#343×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#1738	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₀₇	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₁₀₇	C₂²	1	1	yes	characteristic
12	#575×C₁₀₇	—	2	4	no	—
13	#575×C₁₀₇	C₄	1	8	yes	complemented
14	C₂×#137×C₁₀₇	—	2	1	no	—
15	C₂×#137×C₁₀₇	C₂²	1	2	yes	—
16	C₂×AGL(1,ℤ/8)×C₁₀₇	—	2	1	no	—
17	C₂×AGL(1,ℤ/8)×C₁₀₇	C₂²	1	2	yes	—
18	C₂×#135×C₁₀₇	—	2	2	no	—
19	#568×C₁₀₇	—	2	4	no	—
20	#568×C₁₀₇	—	2	4	no	—
21	C₂×#131×C₁₀₇	—	2	2	no	—
22	C₂×#131×C₁₀₇	C₂²	1	4	yes	—
23	C₂²×M₁₆×C₁₀₇	—	2	2	no	—
24	C₂²×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
29	#417×C₁₀₇	—	2	2	no	—
30	#417×C₁₀₇	—	2	2	no	—
31	#417×C₁₀₇	—	2	2	no	—
32	#417×C₁₀₇	C₂²	1	4	yes	—
33	C₂×#103×C₁₀₇	—	2	1	no	—
34	C₂×#103×C₁₀₇	C₂²	1	2	yes	complemented
35	C₂×#102×C₁₀₇	—	2	1	no	—
36	C₂×#102×C₁₀₇	C₂²	1	2	yes	complemented
37	#413×C₁₀₇	—	2	4	no	—
38	C₂×#101×C₁₀₇	C₂²	1	2	yes	complemented
39	C₂×#100×C₁₀₇	C₂²	1	2	yes	complemented
40	#343×C₁₀₇	C₂²	1	4	yes	complemented
41	#341×C₁₀₇	C₂²	1	4	yes	complemented
42	C₂×#41×C₁₀₇	—	2	1	no	—
43	C₂×#41×C₁₀₇	—	2	2	no	—
44	C₂×#41×C₁₀₇	—	2	2	no	—
45	C₂×#41×C₁₀₇	—	2	2	no	—
46	C₂×#41×C₁₀₇	—	2	1	no	—
47	C₂×#41×C₁₀₇	—	2	1	no	—
48	C₂×#41×C₁₀₇	—	2	1	no	—
49	C₂×#41×C₁₀₇	—	2	1	no	—
50	C₂×#41×C₁₀₇	—	2	1	no	—
51	C₂×#41×C₁₀₇	—	2	2	no	—
52	C₂×#41×C₁₀₇	—	2	2	no	—
53	C₂×#41×C₁₀₇	C₂×C₄	1	4	yes	—
54	C₂×#41×C₁₀₇	C₂×C₄	1	4	yes	—
55	C₂×#41×C₁₀₇	D₄	1	4	yes	—
56	C₂×#41×C₁₀₇	D₄	1	2	yes	—
57	C₂×#41×C₁₀₇	C₂³	1	2	yes	—
58	C₂²×Q₈×C₁₀₇	D₄	1	1	yes	characteristic
59	C₂²×Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₀₇	—	2	1	no	—
61	C₂²×D₄×C₁₀₇	—	2	1	no	—
62	C₂²×D₄×C₁₀₇	D₄	1	1	yes	characteristic
63	C₂²×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₀₇	—	2	1	no	—
65	C₂³×C₄×C₁₀₇	—	2	1	no	—
66	C₂³×C₄×C₁₀₇	—	2	1	no	—
67	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
68	#137×C₁₀₇	—	2	4	no	—
69	#137×C₁₀₇	—	2	8	no	—
70	#137×C₁₀₇	C₂×C₄	1	8	yes	complemented
71	AGL(1,ℤ/8)×C₁₀₇	—	2	4	no	—
72	AGL(1,ℤ/8)×C₁₀₇	—	2	8	no	—
73	AGL(1,ℤ/8)×C₁₀₇	C₂×C₄	1	8	yes	complemented
74	#135×C₁₀₇	—	2	16	no	—
75	C₂×Q₁₆×C₁₀₇	—	2	2	no	—
76	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
77	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
78	C₂×D₈×C₁₀₇	—	2	2	no	—
79	#131×C₁₀₇	—	2	16	no	—
80	#131×C₁₀₇	—	2	8	no	—
81	#131×C₁₀₇	—	2	8	no	—
82	C₂×M₁₆×C₁₀₇	—	2	16	no	—
83	C₂×M₁₆×C₁₀₇	—	2	1	no	—
84	C₂×M₁₆×C₁₀₇	—	2	2	no	—
85	C₂×M₁₆×C₁₀₇	—	2	2	no	—
86	C₂×M₁₆×C₁₀₇	—	2	2	no	—
87	C₂×M₁₆×C₁₀₇	—	2	1	no	—
88	C₂×M₁₆×C₁₀₇	—	2	2	no	—
89	C₂×M₁₆×C₁₀₇	—	2	1	no	—
90	C₂×M₁₆×C₁₀₇	—	2	4	no	—
91	C₂×M₁₆×C₁₀₇	—	2	2	no	—
92	C₂×M₁₆×C₁₀₇	—	2	2	no	—
93	C₂×M₁₆×C₁₀₇	C₂×C₄	1	4	yes	—
94	C₂×M₁₆×C₁₀₇	D₄	1	4	yes	—
95	C₂×M₁₆×C₁₀₇	D₄	1	2	yes	—
96	C₂×M₁₆×C₁₀₇	D₄	1	2	yes	—
97	C₂×M₁₆×C₁₀₇	C₂³	1	2	yes	—
98	C₂×M₁₆×C₁₀₇	C₂³	1	2	yes	—
99	C₂×M₁₆×C₁₀₇	C₂³	1	2	yes	—
100	C₂²×C₈×C₁₀₇	—	2	1	no	—
101	C₂²×C₈×C₁₀₇	—	2	1	no	—
102	C₂²×C₈×C₁₀₇	—	2	4	no	—
103	C₂²×C₈×C₁₀₇	—	2	1	no	—
104	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
111	#103×C₁₀₇	—	2	4	no	—
112	#103×C₁₀₇	—	2	4	no	—
113	#102×C₁₀₇	—	2	4	no	—
114	#102×C₁₀₇	—	2	4	no	—
115	#101×C₁₀₇	—	2	4	no	—
116	#100×C₁₀₇	—	2	4	no	—
117	C₂⁴×C₁₀₇	—	2	1	no	—
118	C₂⁴×C₁₀₇	—	2	1	no	—
119	C₂⁴×C₁₀₇	#41	1	1	yes	characteristic
120	#41×C₁₀₇	—	2	4	no	—
121	#41×C₁₀₇	—	2	4	no	—
122	#41×C₁₀₇	—	2	4	no	—
123	#41×C₁₀₇	—	2	4	no	—
124	#41×C₁₀₇	—	2	4	no	—
125	#41×C₁₀₇	—	2	2	no	—
126	#41×C₁₀₇	—	2	2	no	—
127	#41×C₁₀₇	—	2	4	no	—
128	#41×C₁₀₇	—	2	4	no	—
129	#41×C₁₀₇	—	2	4	no	—
130	#41×C₁₀₇	—	2	4	no	—
131	#41×C₁₀₇	—	4	2	no	—
132	#41×C₁₀₇	—	4	2	no	—
133	#41×C₁₀₇	—	4	2	no	—
134	#41×C₁₀₇	—	4	2	no	—
135	#41×C₁₀₇	C₂²⋊C₄	1	8	yes	—
136	#41×C₁₀₇	C₂²×C₄	1	4	yes	—
137	#41×C₁₀₇	C₂×D₄	1	4	yes	—
138	C₂×Q₈×C₁₀₇	—	2	1	no	—
139	C₂×Q₈×C₁₀₇	—	2	2	no	—
140	C₂×Q₈×C₁₀₇	—	2	1	no	—
141	C₂×Q₈×C₁₀₇	—	2	1	no	—
142	C₂×Q₈×C₁₀₇	—	2	1	no	—
143	C₂×Q₈×C₁₀₇	—	2	1	no	—
144	C₂×Q₈×C₁₀₇	—	2	1	no	—
145	C₂×Q₈×C₁₀₇	C₂²⋊C₄	1	4	yes	—
146	C₂×Q₈×C₁₀₇	C₂²×C₄	1	2	yes	—
147	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₁₀₇	—	2	4	no	—
149	C₂×D₄×C₁₀₇	—	2	2	no	—
150	C₂×D₄×C₁₀₇	—	2	4	no	—
151	C₂×D₄×C₁₀₇	—	2	2	no	—
152	C₂×D₄×C₁₀₇	—	2	4	no	—
153	C₂×D₄×C₁₀₇	—	2	2	no	—
154	C₂×D₄×C₁₀₇	—	2	1	no	—
155	C₂×D₄×C₁₀₇	—	2	1	no	—
156	C₂×D₄×C₁₀₇	—	2	1	no	—
157	C₂×D₄×C₁₀₇	—	2	1	no	—
158	C₂×D₄×C₁₀₇	—	2	1	no	—
159	C₂×D₄×C₁₀₇	—	2	1	no	—
160	C₂×D₄×C₁₀₇	—	4	1	no	—
161	C₂×D₄×C₁₀₇	—	4	1	no	—
162	C₂×D₄×C₁₀₇	—	4	2	no	—
163	C₂×D₄×C₁₀₇	C₂²⋊C₄	1	4	yes	—
164	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
165	C₂×D₄×C₁₀₇	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₀₇	—	2	1	no	—
167	C₂²×C₄×C₁₀₇	—	2	4	no	—
168	C₂²×C₄×C₁₀₇	—	2	4	no	—
169	C₂²×C₄×C₁₀₇	—	2	2	no	—
170	C₂²×C₄×C₁₀₇	—	2	2	no	—
171	C₂²×C₄×C₁₀₇	—	2	1	no	—
172	C₂²×C₄×C₁₀₇	—	2	4	no	—
173	C₂²×C₄×C₁₀₇	—	2	2	no	—
174	C₂²×C₄×C₁₀₇	—	4	1	no	—
175	C₂²×C₄×C₁₀₇	—	4	1	no	—
176	C₂²×C₄×C₁₀₇	—	4	2	no	—
177	C₂²×C₄×C₁₀₇	—	4	1	no	—
178	C₂²×C₄×C₁₀₇	—	4	1	no	—
179	C₂²×C₄×C₁₀₇	—	8	2	no	—
180	C₂²×C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
181	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
188	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
189	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
190	Q₁₆×C₁₀₇	—	2	8	no	—
191	SD₁₆×C₁₀₇	—	2	8	no	—
192	SD₁₆×C₁₀₇	—	2	8	no	—
193	D₈×C₁₀₇	—	2	8	no	—
194	M₁₆×C₁₀₇	—	2	16	no	—
195	M₁₆×C₁₀₇	—	2	4	no	—
196	M₁₆×C₁₀₇	—	2	4	no	—
197	M₁₆×C₁₀₇	—	2	4	no	—
198	M₁₆×C₁₀₇	—	2	4	no	—
199	M₁₆×C₁₀₇	—	2	2	no	—
200	M₁₆×C₁₀₇	—	2	2	no	—
201	M₁₆×C₁₀₇	—	2	2	no	—
202	M₁₆×C₁₀₇	—	2	2	no	—
203	M₁₆×C₁₀₇	—	4	2	no	—
204	M₁₆×C₁₀₇	C₂²×C₄	1	4	yes	—
205	M₁₆×C₁₀₇	C₂×D₄	1	4	yes	—
206	C₂×C₈×C₁₀₇	—	2	16	no	—
207	C₂×C₈×C₁₀₇	—	2	4	no	—
208	C₂×C₈×C₁₀₇	—	2	4	no	—
209	C₂×C₈×C₁₀₇	—	2	2	no	—
210	C₂×C₈×C₁₀₇	—	2	2	no	—
211	C₂×C₈×C₁₀₇	—	2	2	no	—
212	C₂×C₈×C₁₀₇	—	2	2	no	—
213	C₂×C₈×C₁₀₇	—	2	2	no	—
214	C₂×C₈×C₁₀₇	—	4	2	no	—
215	C₂×C₈×C₁₀₇	C₂×D₄	1	4	yes	—
216	C₄⋊C₄×C₁₀₇	—	2	2	no	—
217	C₄⋊C₄×C₁₀₇	—	2	2	no	—
218	C₄⋊C₄×C₁₀₇	—	4	1	no	—
219	C₄⋊C₄×C₁₀₇	—	4	1	no	—
220	C₂³×C₁₀₇	—	2	2	no	—
221	C₂³×C₁₀₇	—	2	4	no	—
222	C₂³×C₁₀₇	—	2	2	no	—
223	C₂³×C₁₀₇	—	4	1	no	—
224	C₂³×C₁₀₇	—	4	1	no	—
225	C₂³×C₁₀₇	—	4	1	no	—
226	C₂³×C₁₀₇	—	4	1	no	—
227	C₂³×C₁₀₇	—	8	1	no	—
228	C₂³×C₁₀₇	—	8	1	no	—
229	C₂³×C₁₀₇	—	8	1	no	—
230	C₂³×C₁₀₇	—	8	1	no	—
231	C₂³×C₁₀₇	C₄×D₄	1	2	yes	—
232	C₂³×C₁₀₇	#121	1	1	yes	characteristic
233	C₂³×C₁₀₇	#121	1	1	yes	characteristic
234	C₂³×C₁₀₇	#123	1	2	yes	—
235	C₂³×C₁₀₇	C₂×#41	1	1	yes	characteristic
236	Q₈×C₁₀₇	—	2	2	no	—
237	Q₈×C₁₀₇	—	2	4	no	—
238	Q₈×C₁₀₇	—	2	2	no	—
239	Q₈×C₁₀₇	—	2	2	no	—
240	Q₈×C₁₀₇	—	4	1	no	—
241	Q₈×C₁₀₇	—	4	1	no	—
242	Q₈×C₁₀₇	C₂×C₂²⋊C₄	1	4	yes	—
243	D₄×C₁₀₇	—	2	4	no	—
244	D₄×C₁₀₇	—	2	4	no	—
245	D₄×C₁₀₇	—	2	8	no	—
246	D₄×C₁₀₇	—	2	2	no	—
247	D₄×C₁₀₇	—	2	2	no	—
248	D₄×C₁₀₇	—	2	2	no	—
249	D₄×C₁₀₇	—	2	4	no	—
250	D₄×C₁₀₇	—	4	4	no	—
251	D₄×C₁₀₇	—	4	4	no	—
252	D₄×C₁₀₇	—	4	1	no	—
253	D₄×C₁₀₇	—	4	1	no	—
254	D₄×C₁₀₇	C₂×C₂²⋊C₄	1	4	yes	—
255	C₂×C₄×C₁₀₇	—	2	2	no	—
256	C₂×C₄×C₁₀₇	—	2	4	no	—
257	C₂×C₄×C₁₀₇	—	2	4	no	—
258	C₂×C₄×C₁₀₇	—	2	4	no	—
259	C₂×C₄×C₁₀₇	—	2	8	no	—
260	C₂×C₄×C₁₀₇	—	2	2	no	—
261	C₂×C₄×C₁₀₇	—	4	1	no	—
262	C₂×C₄×C₁₀₇	—	4	1	no	—
263	C₂×C₄×C₁₀₇	—	4	4	no	—
264	C₂×C₄×C₁₀₇	—	4	4	no	—
265	C₂×C₄×C₁₀₇	—	4	2	no	—
266	C₂×C₄×C₁₀₇	—	8	2	no	—
267	C₂×C₄×C₁₀₇	—	8	2	no	—
268	C₂×C₄×C₁₀₇	—	8	2	no	—
269	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
272	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
273	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
274	C₂×C₄×C₁₀₇	#120	1	2	yes	—
275	C₂×C₄×C₁₀₇	#120	1	2	yes	—
276	C₂×C₄×C₁₀₇	#121	1	2	yes	—
277	C₂×C₄×C₁₀₇	#121	1	2	yes	—
278	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
279	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
280	C₂×C₄×C₁₀₇	#123	1	2	yes	—
281	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
282	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
287	C₈×C₁₀₇	—	2	4	no	—
288	C₈×C₁₀₇	—	2	4	no	—
289	C₈×C₁₀₇	—	2	4	no	—
290	C₈×C₁₀₇	—	4	2	no	—
291	C₂²×C₁₀₇	—	2	1	no	—
292	C₂²×C₁₀₇	—	2	1	no	—
293	C₂²×C₁₀₇	—	2	1	no	—
294	C₂²×C₁₀₇	—	2	1	no	—
295	C₂²×C₁₀₇	—	2	1	no	—
296	C₂²×C₁₀₇	—	2	1	no	—
297	C₂²×C₁₀₇	—	2	4	no	—
298	C₂²×C₁₀₇	—	4	2	no	—
299	C₂²×C₁₀₇	—	4	2	no	—
300	C₂²×C₁₀₇	—	4	2	no	—
301	C₂²×C₁₀₇	—	4	2	no	—
302	C₂²×C₁₀₇	—	4	2	no	—
303	C₂²×C₁₀₇	—	8	4	no	—
304	C₂²×C₁₀₇	—	8	2	no	—
305	C₂²×C₁₀₇	—	8	2	no	—
306	C₂²×C₁₀₇	—	8	1	no	—
307	C₂²×C₁₀₇	—	8	1	no	—
308	C₂²×C₁₀₇	#386	1	2	yes	—
309	C₂²×C₁₀₇	#386	1	2	yes	—
310	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
311	C₂²×C₁₀₇	C₂×#121	1	1	yes	characteristic
312	C₂²×C₁₀₇	C₂×#123	1	1	yes	characteristic
313	C₄×C₁₀₇	—	2	4	no	—
314	C₄×C₁₀₇	—	4	2	no	—
315	C₄×C₁₀₇	—	8	2	no	—
316	C₄×C₁₀₇	#386	1	2	yes	—
317	C₄×C₁₀₇	#386	1	2	yes	—
318	C₄×C₁₀₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
319	C₄×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
320	C₄×C₁₀₇	C₂×#120	1	1	yes	characteristic
321	C₄×C₁₀₇	C₂×#121	1	1	yes	characteristic
322	#21004	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
323	C₂×C₁₀₇	—	2	1	no	—
324	C₂×C₁₀₇	—	2	1	no	—
325	C₂×C₁₀₇	—	2	2	no	—
326	C₂×C₁₀₇	—	2	2	no	—
327	C₂×C₁₀₇	—	4	4	no	—
328	C₂×C₁₀₇	—	8	2	no	—
329	C₂×C₁₀₇	C₂×#386	1	1	yes	characteristic
330	C₂×C₁₀₇	#3068	1	1	yes	characteristic
331	C₂×C₁₀₇	#3069	1	1	yes	characteristic
332	C₂×#575	C₂×C₁₀₇	1	1	yes	characteristic
333	C₂×#568	C₂×C₁₀₇	1	1	yes	characteristic, complemented
334	C₂×#417	C₂×C₁₀₇	1	1	yes	characteristic, complemented
335	C₂×#417	C₂×C₁₀₇	1	1	yes	characteristic, complemented
336	C₂×#413	C₂×C₁₀₇	1	1	yes	characteristic, complemented
337	#1908	C₂×C₁₀₇	1	4	yes	complemented
338	#1907	C₂×C₁₀₇	1	4	yes	complemented
339	C₂×#343	C₂×C₁₀₇	1	1	yes	characteristic, complemented
340	#1738	C₂×C₁₀₇	1	1	yes	characteristic, complemented
341	C₁₀₇	#21004	1	1	yes	characteristic, direct product factor, Sylow
342	C₂²×#41	C₂²×C₁₀₇	1	1	yes	characteristic
343	C₂²×#41	C₂²×C₁₀₇	1	1	yes	characteristic
344	#575	—	2	4	no	—
345	#575	C₄×C₁₀₇	1	8	yes	complemented
346	C₂×#137	—	2	1	no	—
347	C₂×#137	C₂²×C₁₀₇	1	2	yes	—
348	C₂×AGL(1,ℤ/8)	—	2	1	no	—
349	C₂×AGL(1,ℤ/8)	C₂²×C₁₀₇	1	2	yes	—
350	C₂×#135	—	2	2	no	—
351	#568	—	2	4	no	—
352	#568	—	2	4	no	—
353	C₂×#131	—	2	2	no	—
354	C₂×#131	C₂²×C₁₀₇	1	4	yes	—
355	C₂²×M₁₆	—	2	2	no	—
356	C₂²×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
357	C₂²×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
358	C₂²×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
359	C₂²×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
360	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
361	#417	—	2	2	no	—
362	#417	—	2	2	no	—
363	#417	—	2	2	no	—
364	#417	C₂²×C₁₀₇	1	4	yes	—
365	C₂×#103	—	2	1	no	—
366	C₂×#103	C₂²×C₁₀₇	1	2	yes	complemented
367	C₂×#102	—	2	1	no	—
368	C₂×#102	C₂²×C₁₀₇	1	2	yes	complemented
369	#413	—	2	4	no	—
370	C₂×#101	C₂²×C₁₀₇	1	2	yes	complemented
371	C₂×#100	C₂²×C₁₀₇	1	2	yes	complemented
372	#343	C₂²×C₁₀₇	1	4	yes	complemented
373	#341	C₂²×C₁₀₇	1	4	yes	complemented
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	2	no	—
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	2	no	—
378	C₂×#41	—	2	1	no	—
379	C₂×#41	—	2	1	no	—
380	C₂×#41	—	2	1	no	—
381	C₂×#41	—	2	2	no	—
382	C₂×#41	—	2	1	no	—
383	C₂×#41	—	2	1	no	—
384	C₂×#41	—	2	2	no	—
385	C₂×#41	C₂×C₄×C₁₀₇	1	4	yes	—
386	C₂×#41	C₂×C₄×C₁₀₇	1	4	yes	—
387	C₂×#41	D₄×C₁₀₇	1	4	yes	—
388	C₂×#41	D₄×C₁₀₇	1	2	yes	—
389	C₂×#41	C₂³×C₁₀₇	1	2	yes	—
390	C₂²×Q₈	D₄×C₁₀₇	1	1	yes	characteristic
391	C₂²×Q₈	C₂³×C₁₀₇	1	1	yes	characteristic
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	D₄×C₁₀₇	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₁₀₇	1	1	yes	characteristic
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	—	2	1	no	—
399	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
400	#137	—	2	4	no	—
401	#137	—	2	8	no	—
402	#137	C₂×C₄×C₁₀₇	1	8	yes	complemented
403	AGL(1,ℤ/8)	—	2	4	no	—
404	AGL(1,ℤ/8)	—	2	8	no	—
405	AGL(1,ℤ/8)	C₂×C₄×C₁₀₇	1	8	yes	complemented
406	#135	—	2	16	no	—
407	C₂×Q₁₆	—	2	2	no	—
408	C₂×SD₁₆	—	2	2	no	—
409	C₂×SD₁₆	—	2	2	no	—
410	C₂×D₈	—	2	2	no	—
411	#131	—	2	16	no	—
412	#131	—	2	8	no	—
413	#131	—	2	8	no	—
414	C₂×M₁₆	—	2	16	no	—
415	C₂×M₁₆	—	2	1	no	—
416	C₂×M₁₆	—	2	2	no	—
417	C₂×M₁₆	—	2	2	no	—
418	C₂×M₁₆	—	2	2	no	—
419	C₂×M₁₆	—	2	1	no	—
420	C₂×M₁₆	—	2	2	no	—
421	C₂×M₁₆	—	2	1	no	—
422	C₂×M₁₆	—	2	4	no	—
423	C₂×M₁₆	—	2	2	no	—
424	C₂×M₁₆	—	2	2	no	—
425	C₂×M₁₆	C₂×C₄×C₁₀₇	1	4	yes	—
426	C₂×M₁₆	D₄×C₁₀₇	1	4	yes	—
427	C₂×M₁₆	D₄×C₁₀₇	1	2	yes	—
428	C₂×M₁₆	D₄×C₁₀₇	1	2	yes	—
429	C₂×M₁₆	C₂³×C₁₀₇	1	2	yes	—
430	C₂×M₁₆	C₂³×C₁₀₇	1	2	yes	—
431	C₂×M₁₆	C₂³×C₁₀₇	1	2	yes	—
432	C₂²×C₈	—	2	1	no	—
433	C₂²×C₈	—	2	1	no	—
434	C₂²×C₈	—	2	4	no	—
435	C₂²×C₈	—	2	1	no	—
436	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
443	#103	—	2	4	no	—
444	#103	—	2	4	no	—
445	#102	—	2	4	no	—
446	#102	—	2	4	no	—
447	#101	—	2	4	no	—
448	#100	—	2	4	no	—
449	C₂⁴	—	2	1	no	—
450	C₂⁴	—	2	1	no	—
451	C₂⁴	#41×C₁₀₇	1	1	yes	characteristic
452	#41	—	2	4	no	—
453	#41	—	2	4	no	—
454	#41	—	2	4	no	—
455	#41	—	2	4	no	—
456	#41	—	2	4	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	2	4	no	—
460	#41	—	2	4	no	—
461	#41	—	2	4	no	—
462	#41	—	2	4	no	—
463	#41	—	4	2	no	—
464	#41	—	4	2	no	—
465	#41	—	4	2	no	—
466	#41	—	4	2	no	—
467	#41	C₂²⋊C₄×C₁₀₇	1	8	yes	—
468	#41	C₂²×C₄×C₁₀₇	1	4	yes	—
469	#41	C₂×D₄×C₁₀₇	1	4	yes	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	C₂²⋊C₄×C₁₀₇	1	4	yes	—
478	C₂×Q₈	C₂²×C₄×C₁₀₇	1	2	yes	—
479	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	4	1	no	—
493	C₂×D₄	—	4	1	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	C₂²⋊C₄×C₁₀₇	1	4	yes	—
496	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
497	C₂×D₄	C₂×D₄×C₁₀₇	1	2	yes	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	—	4	1	no	—
511	C₂²×C₄	—	8	2	no	—
512	C₂²×C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
513	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
514	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
519	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
520	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
522	Q₁₆	—	2	8	no	—
523	SD₁₆	—	2	8	no	—
524	SD₁₆	—	2	8	no	—
525	D₈	—	2	8	no	—
526	M₁₆	—	2	16	no	—
527	M₁₆	—	2	4	no	—
528	M₁₆	—	2	4	no	—
529	M₁₆	—	2	4	no	—
530	M₁₆	—	2	4	no	—
531	M₁₆	—	2	2	no	—
532	M₁₆	—	2	2	no	—
533	M₁₆	—	2	2	no	—
534	M₁₆	—	2	2	no	—
535	M₁₆	—	4	2	no	—
536	M₁₆	C₂²×C₄×C₁₀₇	1	4	yes	—
537	M₁₆	C₂×D₄×C₁₀₇	1	4	yes	—
538	C₂×C₈	—	2	16	no	—
539	C₂×C₈	—	2	4	no	—
540	C₂×C₈	—	2	4	no	—
541	C₂×C₈	—	2	2	no	—
542	C₂×C₈	—	2	2	no	—
543	C₂×C₈	—	2	2	no	—
544	C₂×C₈	—	2	2	no	—
545	C₂×C₈	—	2	2	no	—
546	C₂×C₈	—	4	2	no	—
547	C₂×C₈	C₂×D₄×C₁₀₇	1	4	yes	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	8	1	no	—
560	C₂³	—	8	1	no	—
561	C₂³	—	8	1	no	—
562	C₂³	—	8	1	no	—
563	C₂³	C₄×D₄×C₁₀₇	1	2	yes	—
564	C₂³	#121×C₁₀₇	1	1	yes	characteristic
565	C₂³	#121×C₁₀₇	1	1	yes	characteristic
566	C₂³	#123×C₁₀₇	1	2	yes	—
567	C₂³	C₂×#41×C₁₀₇	1	1	yes	characteristic
568	Q₈	—	2	4	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	2	2	no	—
571	Q₈	—	2	2	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	C₂×C₂²⋊C₄×C₁₀₇	1	4	yes	—
575	D₄	—	2	8	no	—
576	D₄	—	2	4	no	—
577	D₄	—	2	4	no	—
578	D₄	—	2	4	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	4	no	—
583	D₄	—	4	4	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	C₂×C₂²⋊C₄×C₁₀₇	1	4	yes	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	8	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	8	2	no	—
599	C₂×C₄	—	8	2	no	—
600	C₂×C₄	—	8	2	no	—
601	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	2	yes	—
602	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	2	yes	—
603	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
604	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
605	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
606	C₂×C₄	#120×C₁₀₇	1	2	yes	—
607	C₂×C₄	#120×C₁₀₇	1	2	yes	—
608	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
609	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
610	C₂×C₄	#121×C₁₀₇	1	2	yes	—
611	C₂×C₄	#121×C₁₀₇	1	2	yes	—
612	C₂×C₄	#123×C₁₀₇	1	2	yes	—
613	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
614	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
615	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
616	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
617	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
618	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
619	C₈	—	2	4	no	—
620	C₈	—	2	4	no	—
621	C₈	—	2	4	no	—
622	C₈	—	4	2	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	8	4	no	—
636	C₂²	—	8	2	no	—
637	C₂²	—	8	2	no	—
638	C₂²	—	8	1	no	—
639	C₂²	—	8	1	no	—
640	C₂²	#386×C₁₀₇	1	2	yes	—
641	C₂²	#386×C₁₀₇	1	2	yes	—
642	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
643	C₂²	C₂×#121×C₁₀₇	1	1	yes	characteristic
644	C₂²	C₂×#123×C₁₀₇	1	1	yes	characteristic
645	C₄	—	2	4	no	—
646	C₄	—	4	2	no	—
647	C₄	—	8	2	no	—
648	C₄	#386×C₁₀₇	1	2	yes	—
649	C₄	#386×C₁₀₇	1	2	yes	—
650	C₄	C₂²×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
651	C₄	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
652	C₄	C₂×#120×C₁₀₇	1	1	yes	characteristic
653	C₄	C₂×#121×C₁₀₇	1	1	yes	characteristic
654	C₂	—	2	2	no	—
655	C₂	—	2	1	no	—
656	C₂	—	2	1	no	—
657	C₂	—	2	2	no	—
658	C₂	—	4	4	no	—
659	C₂	—	8	2	no	—
660	C₂	C₂×#386×C₁₀₇	1	1	yes	characteristic
661	C₂	C₁₀₇×#3068	1	1	yes	characteristic
662	C₂	C₁₀₇×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₁₀₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
prime radical	C₂×#575×C₁₀₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂³×C₄×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#568×C₁₀₇	C₂	semidirect
3. C₂×#417×C₁₀₇	C₂	semidirect
4. C₂×#417×C₁₀₇	C₂	semidirect
5. C₂×#413×C₁₀₇	C₂	semidirect
6. C₁₀₇×#1908	C₂	semidirect
7. C₁₀₇×#1907	C₂	semidirect
8. C₂×#343×C₁₀₇	C₂	semidirect
9. C₁₀₇×#1738	C₂	semidirect
13. #575×C₁₀₇	C₄	semidirect
34. C₂×#103×C₁₀₇	C₂²	semidirect
36. C₂×#102×C₁₀₇	C₂²	semidirect
38. C₂×#101×C₁₀₇	C₂²	semidirect
39. C₂×#100×C₁₀₇	C₂²	semidirect
40. #343×C₁₀₇	C₂²	semidirect
41. #341×C₁₀₇	C₂²	semidirect
70. #137×C₁₀₇	C₂×C₄	semidirect
73. AGL(1,ℤ/8)×C₁₀₇	C₂×C₄	semidirect
322. #21004	C₁₀₇	direct (N × H)
333. C₂×#568	C₂×C₁₀₇	semidirect
334. C₂×#417	C₂×C₁₀₇	semidirect
335. C₂×#417	C₂×C₁₀₇	semidirect
336. C₂×#413	C₂×C₁₀₇	semidirect
337. #1908	C₂×C₁₀₇	semidirect
338. #1907	C₂×C₁₀₇	semidirect
339. C₂×#343	C₂×C₁₀₇	semidirect
340. #1738	C₂×C₁₀₇	semidirect
341. C₁₀₇	#21004	direct (N × H)
345. #575	C₄×C₁₀₇	semidirect
366. C₂×#103	C₂²×C₁₀₇	semidirect
368. C₂×#102	C₂²×C₁₀₇	semidirect
370. C₂×#101	C₂²×C₁₀₇	semidirect
371. C₂×#100	C₂²×C₁₀₇	semidirect
372. #343	C₂²×C₁₀₇	semidirect
373. #341	C₂²×C₁₀₇	semidirect
402. #137	C₂×C₄×C₁₀₇	semidirect
405. AGL(1,ℤ/8)	C₂×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×#575×C₁₀₇	2
C₂×#568×C₁₀₇	2
C₂×#417×C₁₀₇	2
C₂×#413×C₁₀₇	2
C₁₀₇×#1908	2
C₁₀₇×#1907	2
C₂×#343×C₁₀₇	2
C₁₀₇×#1738	2
#21004	107

Subgroups — C107×#21004 #41046968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#21004 #41046968