Subgroups — C₁₀₇×#22566 #41048530

Order 27392.

1178 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#102×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇×#2345	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊C₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1936	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#1925	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#1862	C₂	1	2	yes	maximal, complemented
7	C₁₀₇×#1824	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₇×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#1786	C₂	1	1	yes	maximal, characteristic
10	C₁₀₇×#1762	C₂	1	2	yes	maximal, complemented
11	C₁₀₇×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₀₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
17	C₂×#107×C₁₀₇	C₂²	1	2	yes	complemented
18	C₂×#102×C₁₀₇	C₄	1	8	yes	complemented
19	C₂×#102×C₁₀₇	C₂²	1	2	yes	—
20	C₂×#102×C₁₀₇	C₂²	1	2	yes	—
21	C₂×#102×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×#102×C₁₀₇	C₂²	1	1	yes	characteristic
23	C₂×#102×C₁₀₇	C₂²	1	1	yes	characteristic
24	C₂×#102×C₁₀₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
26	C₂×#97×C₁₀₇	C₂²	1	2	yes	complemented
27	#390×C₁₀₇	C₂²	1	2	yes	—
28	#389×C₁₀₇	C₂²	1	2	yes	complemented
29	#387×C₁₀₇	—	2	2	no	—
30	#386×C₁₀₇	—	2	2	no	—
31	#380×C₁₀₇	—	2	1	no	—
32	#380×C₁₀₇	C₂²	1	1	yes	characteristic
33	#380×C₁₀₇	C₂²	1	1	yes	characteristic
34	#379×C₁₀₇	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	complemented
36	C₄×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
37	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
38	#340×C₁₀₇	C₂²	1	2	yes	complemented
39	#340×C₁₀₇	C₂²	1	2	yes	complemented
40	#340×C₁₀₇	C₂²	1	2	yes	complemented
41	#336×C₁₀₇	C₂²	1	2	yes	complemented
42	C₂⁵×C₁₀₇	—	2	1	no	—
43	C₂²×D₄×C₁₀₇	—	2	4	no	—
44	C₂²×D₄×C₁₀₇	—	2	1	no	—
45	C₂²×D₄×C₁₀₇	—	2	2	no	—
46	C₂²×D₄×C₁₀₇	—	4	2	no	—
47	C₂²×D₄×C₁₀₇	C₂×C₄	1	4	yes	—
48	C₂²×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₀₇	—	2	1	no	—
51	C₂³×C₄×C₁₀₇	—	2	2	no	—
52	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₀₇	—	4	2	no	—
54	C₂²×C₈×C₁₀₇	C₂×C₄	1	4	yes	complemented
55	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₀₇	—	2	4	no	—
59	C₄×D₄×C₁₀₇	—	4	2	no	—
60	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	4	yes	complemented
64	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₀₇	—	4	4	no	—
74	C₂×C₂²⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₀₇	—	2	2	no	—
77	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
78	#107×C₁₀₇	—	4	2	no	—
79	#102×C₁₀₇	—	2	4	no	—
80	#102×C₁₀₇	—	4	2	no	—
81	#102×C₁₀₇	C₂×C₄	1	4	yes	—
82	#102×C₁₀₇	C₂×C₄	1	4	yes	—
83	#102×C₁₀₇	C₂×C₄	1	4	yes	complemented
84	#102×C₁₀₇	C₂×C₄	1	4	yes	complemented
85	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
86	#97×C₁₀₇	—	4	2	no	—
87	#95×C₁₀₇	—	2	2	no	—
88	#95×C₁₀₇	—	2	2	no	—
89	#95×C₁₀₇	—	2	1	no	—
90	#95×C₁₀₇	—	2	1	no	—
91	#95×C₁₀₇	D₄	1	2	yes	—
92	C₂⁴×C₁₀₇	—	2	1	no	—
93	C₂⁴×C₁₀₇	—	2	1	no	—
94	C₂⁴×C₁₀₇	—	2	4	no	—
95	C₂⁴×C₁₀₇	—	4	4	no	—
96	C₂⁴×C₁₀₇	—	4	2	no	—
97	C₂⁴×C₁₀₇	—	4	2	no	—
98	C₂⁴×C₁₀₇	—	8	2	no	—
99	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
100	C₂×D₄×C₁₀₇	—	2	8	no	—
101	C₂×D₄×C₁₀₇	—	2	4	no	—
102	C₂×D₄×C₁₀₇	—	2	1	no	—
103	C₂×D₄×C₁₀₇	—	2	2	no	—
104	C₂×D₄×C₁₀₇	—	2	1	no	—
105	C₂×D₄×C₁₀₇	—	2	2	no	—
106	C₂×D₄×C₁₀₇	—	2	2	no	—
107	C₂×D₄×C₁₀₇	—	4	4	no	—
108	C₂×D₄×C₁₀₇	—	4	8	no	—
109	C₂×D₄×C₁₀₇	—	4	4	no	—
110	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₀₇	#41	1	4	yes	—
113	C₂²×C₄×C₁₀₇	—	2	2	no	—
114	C₂²×C₄×C₁₀₇	—	2	2	no	—
115	C₂²×C₄×C₁₀₇	—	2	1	no	—
116	C₂²×C₄×C₁₀₇	—	2	1	no	—
117	C₂²×C₄×C₁₀₇	—	2	4	no	—
118	C₂²×C₄×C₁₀₇	—	2	2	no	—
119	C₂²×C₄×C₁₀₇	—	2	2	no	—
120	C₂²×C₄×C₁₀₇	—	4	4	no	—
121	C₂²×C₄×C₁₀₇	—	4	4	no	—
122	C₂²×C₄×C₁₀₇	—	8	2	no	—
123	C₂²×C₄×C₁₀₇	—	8	2	no	—
124	C₂²×C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
129	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₁₀₇	—	2	2	no	—
131	C₂×C₈×C₁₀₇	—	2	2	no	—
132	C₂×C₈×C₁₀₇	—	2	2	no	—
133	C₂×C₈×C₁₀₇	—	2	2	no	—
134	C₂×C₈×C₁₀₇	—	2	2	no	—
135	C₂×C₈×C₁₀₇	—	4	4	no	—
136	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
138	C₄⋊C₄×C₁₀₇	—	2	4	no	—
139	C₄⋊C₄×C₁₀₇	—	2	1	no	—
140	C₄⋊C₄×C₁₀₇	—	2	1	no	—
141	C₄⋊C₄×C₁₀₇	—	2	2	no	—
142	C₄⋊C₄×C₁₀₇	—	2	2	no	—
143	C₄⋊C₄×C₁₀₇	—	2	2	no	—
144	C₄⋊C₄×C₁₀₇	—	2	2	no	—
145	C₄⋊C₄×C₁₀₇	—	8	2	no	—
146	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
148	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
149	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
150	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
151	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
152	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
153	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
154	C₂²⋊C₄×C₁₀₇	—	8	2	no	—
155	C₄²×C₁₀₇	—	2	2	no	—
156	C₄²×C₁₀₇	—	2	2	no	—
157	C₄²×C₁₀₇	—	8	2	no	—
158	C₂³×C₁₀₇	—	2	2	no	—
159	C₂³×C₁₀₇	—	2	2	no	—
160	C₂³×C₁₀₇	—	2	2	no	—
161	C₂³×C₁₀₇	—	2	4	no	—
162	C₂³×C₁₀₇	—	2	2	no	—
163	C₂³×C₁₀₇	—	4	8	no	—
164	C₂³×C₁₀₇	—	4	1	no	—
165	C₂³×C₁₀₇	—	4	1	no	—
166	C₂³×C₁₀₇	—	4	2	no	—
167	C₂³×C₁₀₇	—	4	2	no	—
168	C₂³×C₁₀₇	—	4	1	no	—
169	C₂³×C₁₀₇	—	4	1	no	—
170	C₂³×C₁₀₇	—	4	2	no	—
171	C₂³×C₁₀₇	—	4	8	no	—
172	C₂³×C₁₀₇	—	8	4	no	—
173	C₂³×C₁₀₇	—	8	8	no	—
174	C₂³×C₁₀₇	—	8	8	no	—
175	C₂³×C₁₀₇	C₄×D₄	1	2	yes	—
176	C₂³×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
177	C₂³×C₁₀₇	#137	1	2	yes	—
178	C₂³×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
179	D₄×C₁₀₇	—	2	2	no	—
180	D₄×C₁₀₇	—	2	2	no	—
181	D₄×C₁₀₇	—	2	2	no	—
182	D₄×C₁₀₇	—	2	4	no	—
183	D₄×C₁₀₇	—	4	8	no	—
184	D₄×C₁₀₇	—	4	2	no	—
185	D₄×C₁₀₇	#117	1	4	yes	—
186	C₂×C₄×C₁₀₇	—	2	2	no	—
187	C₂×C₄×C₁₀₇	—	2	2	no	—
188	C₂×C₄×C₁₀₇	—	2	2	no	—
189	C₂×C₄×C₁₀₇	—	2	4	no	—
190	C₂×C₄×C₁₀₇	—	2	2	no	—
191	C₂×C₄×C₁₀₇	—	2	2	no	—
192	C₂×C₄×C₁₀₇	—	2	2	no	—
193	C₂×C₄×C₁₀₇	—	2	2	no	—
194	C₂×C₄×C₁₀₇	—	2	2	no	—
195	C₂×C₄×C₁₀₇	—	2	2	no	—
196	C₂×C₄×C₁₀₇	—	2	2	no	—
197	C₂×C₄×C₁₀₇	—	2	2	no	—
198	C₂×C₄×C₁₀₇	—	4	2	no	—
199	C₂×C₄×C₁₀₇	—	4	2	no	—
200	C₂×C₄×C₁₀₇	—	4	2	no	—
201	C₂×C₄×C₁₀₇	—	4	2	no	—
202	C₂×C₄×C₁₀₇	—	4	2	no	—
203	C₂×C₄×C₁₀₇	—	4	2	no	—
204	C₂×C₄×C₁₀₇	—	4	2	no	—
205	C₂×C₄×C₁₀₇	—	4	2	no	—
206	C₂×C₄×C₁₀₇	—	8	4	no	—
207	C₂×C₄×C₁₀₇	—	8	8	no	—
208	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₀₇	C₂×#41	1	2	yes	—
211	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
213	C₈×C₁₀₇	—	2	2	no	—
214	C₈×C₁₀₇	—	2	2	no	—
215	C₈×C₁₀₇	—	4	2	no	—
216	C₂²×C₁₀₇	—	2	2	no	—
217	C₂²×C₁₀₇	—	2	2	no	—
218	C₂²×C₁₀₇	—	2	4	no	—
219	C₂²×C₁₀₇	—	2	4	no	—
220	C₂²×C₁₀₇	—	2	4	no	—
221	C₂²×C₁₀₇	—	4	2	no	—
222	C₂²×C₁₀₇	—	4	2	no	—
223	C₂²×C₁₀₇	—	4	4	no	—
224	C₂²×C₁₀₇	—	4	4	no	—
225	C₂²×C₁₀₇	—	4	2	no	—
226	C₂²×C₁₀₇	—	4	2	no	—
227	C₂²×C₁₀₇	—	4	2	no	—
228	C₂²×C₁₀₇	—	8	16	no	—
229	C₂²×C₁₀₇	—	8	2	no	—
230	C₂²×C₁₀₇	—	8	2	no	—
231	C₂²×C₁₀₇	#440	1	4	yes	—
232	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
233	C₂²×C₁₀₇	#546	1	2	yes	—
234	C₂²×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂²×C₁₀₇	C₂×#137	1	1	yes	characteristic
236	C₂²×C₁₀₇	#576	1	2	yes	—
237	C₄×C₁₀₇	—	2	2	no	—
238	C₄×C₁₀₇	—	4	2	no	—
239	C₄×C₁₀₇	—	4	2	no	—
240	C₄×C₁₀₇	—	4	2	no	—
241	C₄×C₁₀₇	—	4	2	no	—
242	C₄×C₁₀₇	—	8	2	no	—
243	C₄×C₁₀₇	—	8	2	no	—
244	C₄×C₁₀₇	C₂×#117	1	1	yes	characteristic
245	C₄×C₁₀₇	#518	1	1	yes	characteristic
246	C₄×C₁₀₇	#551	1	2	yes	—
247	#22566	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂×C₁₀₇	—	2	4	no	—
249	C₂×C₁₀₇	—	4	4	no	—
250	C₂×C₁₀₇	—	8	2	no	—
251	C₂×C₁₀₇	#2342	1	1	yes	characteristic
252	C₂×C₁₀₇	C₂×#440	1	1	yes	characteristic
253	C₂×C₁₀₇	#2948	1	1	yes	characteristic
254	C₂×C₁₀₇	#3314	1	2	yes	—
255	C₂×C₁₀₇	#3318	1	2	yes	—
256	C₂²×#102	C₂×C₁₀₇	1	1	yes	characteristic
257	#2345	C₂×C₁₀₇	1	1	yes	characteristic, complemented
258	D₄×C₂²⋊C₄	C₂×C₁₀₇	1	1	yes	characteristic
259	#1936	C₂×C₁₀₇	1	2	yes	complemented
260	#1925	C₂×C₁₀₇	1	2	yes	complemented
261	#1862	C₂×C₁₀₇	1	2	yes	complemented
262	#1824	C₂×C₁₀₇	1	1	yes	characteristic, complemented
263	#1808	C₂×C₁₀₇	1	1	yes	characteristic, complemented
264	#1786	C₂×C₁₀₇	1	1	yes	characteristic
265	#1762	C₂×C₁₀₇	1	2	yes	complemented
266	#1752	C₂×C₁₀₇	1	1	yes	characteristic, complemented
267	C₁₀₇	#22566	1	1	yes	characteristic, direct product factor, Sylow
268	C₂³×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
269	C₂³×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₁₀₇	1	2	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	—	2	1	no	—
273	C₂×#107	C₂²×C₁₀₇	1	2	yes	complemented
274	C₂×#102	C₄×C₁₀₇	1	8	yes	complemented
275	C₂×#102	C₂²×C₁₀₇	1	2	yes	—
276	C₂×#102	C₂²×C₁₀₇	1	2	yes	—
277	C₂×#102	C₂²×C₁₀₇	1	1	yes	characteristic
278	C₂×#102	C₂²×C₁₀₇	1	1	yes	characteristic
279	C₂×#102	C₂²×C₁₀₇	1	1	yes	characteristic
280	C₂×#102	C₂²×C₁₀₇	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
282	C₂×#97	C₂²×C₁₀₇	1	2	yes	complemented
283	#390	C₂²×C₁₀₇	1	2	yes	—
284	#389	C₂²×C₁₀₇	1	2	yes	complemented
285	#387	—	2	2	no	—
286	#386	—	2	2	no	—
287	#380	—	2	1	no	—
288	#380	C₂²×C₁₀₇	1	1	yes	characteristic
289	#380	C₂²×C₁₀₇	1	1	yes	characteristic
290	#379	—	2	1	no	—
291	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	complemented
292	C₄×C₂²⋊C₄	—	2	1	no	—
293	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
294	#340	C₂²×C₁₀₇	1	2	yes	complemented
295	#340	C₂²×C₁₀₇	1	2	yes	complemented
296	#340	C₂²×C₁₀₇	1	2	yes	complemented
297	#336	C₂²×C₁₀₇	1	2	yes	complemented
298	C₂⁵	—	2	1	no	—
299	C₂²×D₄	—	2	4	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	4	2	no	—
303	C₂²×D₄	C₂×C₄×C₁₀₇	1	4	yes	—
304	C₂²×D₄	C₂³×C₁₀₇	1	1	yes	characteristic
305	C₂²×D₄	C₂³×C₁₀₇	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
309	C₂²×C₈	—	4	2	no	—
310	C₂²×C₈	C₂×C₄×C₁₀₇	1	4	yes	complemented
311	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
312	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	4	2	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	4	yes	complemented
320	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	4	4	no	—
330	C₂×C₂²⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
332	C₂×C₄²	—	2	2	no	—
333	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
334	#107	—	4	2	no	—
335	#102	—	2	4	no	—
336	#102	—	4	2	no	—
337	#102	C₂×C₄×C₁₀₇	1	4	yes	—
338	#102	C₂×C₄×C₁₀₇	1	4	yes	—
339	#102	C₂×C₄×C₁₀₇	1	4	yes	complemented
340	#102	C₂×C₄×C₁₀₇	1	4	yes	complemented
341	C₂²⋊C₈	—	2	2	no	—
342	#97	—	4	2	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	#95	D₄×C₁₀₇	1	2	yes	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	2	1	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	4	4	no	—
352	C₂⁴	—	4	2	no	—
353	C₂⁴	—	4	2	no	—
354	C₂⁴	—	8	2	no	—
355	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	4	8	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
367	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
368	C₂×D₄	#41×C₁₀₇	1	4	yes	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	4	no	—
378	C₂²×C₄	—	8	2	no	—
379	C₂²×C₄	—	8	2	no	—
380	C₂²×C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
383	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
384	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	4	4	no	—
392	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
393	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	8	2	no	—
402	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
403	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	—	4	2	no	—
410	C₂²⋊C₄	—	8	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	8	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	4	8	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	8	4	no	—
429	C₂³	—	8	8	no	—
430	C₂³	—	8	8	no	—
431	C₂³	C₄×D₄×C₁₀₇	1	2	yes	—
432	C₂³	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
433	C₂³	#137×C₁₀₇	1	2	yes	—
434	C₂³	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
435	D₄	—	2	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	2	4	no	—
439	D₄	—	4	8	no	—
440	D₄	—	4	2	no	—
441	D₄	#117×C₁₀₇	1	4	yes	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	8	4	no	—
463	C₂×C₄	—	8	8	no	—
464	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
465	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₁₀₇	1	2	yes	—
467	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
468	C₂×C₄	H(5,𝔽₂)×C₁₀₇	1	2	yes	—
469	C₈	—	2	2	no	—
470	C₈	—	2	2	no	—
471	C₈	—	4	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	8	16	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	#440×C₁₀₇	1	4	yes	—
488	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
489	C₂²	#546×C₁₀₇	1	2	yes	—
490	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
491	C₂²	C₂×#137×C₁₀₇	1	1	yes	characteristic
492	C₂²	#576×C₁₀₇	1	2	yes	—
493	C₄	—	2	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	2	no	—
499	C₄	—	8	2	no	—
500	C₄	C₂×#117×C₁₀₇	1	1	yes	characteristic
501	C₄	#518×C₁₀₇	1	1	yes	characteristic
502	C₄	#551×C₁₀₇	1	2	yes	—
503	C₂	—	2	4	no	—
504	C₂	—	4	4	no	—
505	C₂	—	8	2	no	—
506	C₂	C₁₀₇×#2342	1	1	yes	characteristic
507	C₂	C₂×#440×C₁₀₇	1	1	yes	characteristic
508	C₂	C₁₀₇×#2948	1	1	yes	characteristic
509	C₂	C₁₀₇×#3314	1	2	yes	—
510	C₂	C₁₀₇×#3318	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₀₇×#2345	C₂	semidirect
4. C₁₀₇×#1936	C₂	semidirect
5. C₁₀₇×#1925	C₂	semidirect
6. C₁₀₇×#1862	C₂	semidirect
7. C₁₀₇×#1824	C₂	semidirect
8. C₁₀₇×#1808	C₂	semidirect
10. C₁₀₇×#1762	C₂	semidirect
11. C₁₀₇×#1752	C₂	semidirect
17. C₂×#107×C₁₀₇	C₂²	semidirect
18. C₂×#102×C₁₀₇	C₄	semidirect
26. C₂×#97×C₁₀₇	C₂²	semidirect
28. #389×C₁₀₇	C₂²	semidirect
35. C₄×C₄⋊C₄×C₁₀₇	C₂²	semidirect
38. #340×C₁₀₇	C₂²	semidirect
39. #340×C₁₀₇	C₂²	semidirect
40. #340×C₁₀₇	C₂²	semidirect
41. #336×C₁₀₇	C₂²	semidirect
54. C₂²×C₈×C₁₀₇	C₂×C₄	semidirect
63. C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	semidirect
83. #102×C₁₀₇	C₂×C₄	semidirect
84. #102×C₁₀₇	C₂×C₄	semidirect
247. #22566	C₁₀₇	direct (N × H)
257. #2345	C₂×C₁₀₇	semidirect
259. #1936	C₂×C₁₀₇	semidirect
260. #1925	C₂×C₁₀₇	semidirect
261. #1862	C₂×C₁₀₇	semidirect
262. #1824	C₂×C₁₀₇	semidirect
263. #1808	C₂×C₁₀₇	semidirect
265. #1762	C₂×C₁₀₇	semidirect
266. #1752	C₂×C₁₀₇	semidirect
267. C₁₀₇	#22566	direct (N × H)
273. C₂×#107	C₂²×C₁₀₇	semidirect
274. C₂×#102	C₄×C₁₀₇	semidirect
282. C₂×#97	C₂²×C₁₀₇	semidirect
284. #389	C₂²×C₁₀₇	semidirect
291. C₄×C₄⋊C₄	C₂²×C₁₀₇	semidirect
294. #340	C₂²×C₁₀₇	semidirect
295. #340	C₂²×C₁₀₇	semidirect
296. #340	C₂²×C₁₀₇	semidirect
297. #336	C₂²×C₁₀₇	semidirect
310. C₂²×C₈	C₂×C₄×C₁₀₇	semidirect
319. C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	semidirect
339. #102	C₂×C₄×C₁₀₇	semidirect
340. #102	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
C₂²×#102×C₁₀₇	2
C₁₀₇×#2345	2
D₄×C₂²⋊C₄×C₁₀₇	2
C₁₀₇×#1936	2
C₁₀₇×#1925	2
C₁₀₇×#1862	2
C₁₀₇×#1824	2
C₁₀₇×#1808	2
C₁₀₇×#1786	2
C₁₀₇×#1762	2
C₁₀₇×#1752	2
#22566	107

Subgroups — C107×#22566 #41048530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#22566 #41048530