Group #41039451 — subgroups

Subgroups — C₁₀₇×#13487 #41039451

Order 27392.

338 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#361×C₁₀₇	C₂	1	2	yes	maximal
2	C₁₀₇×#1972	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇×#1849	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#1383	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#1377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₈×C₁₀₇	C₂²	1	1	yes	characteristic
7	C₂×M₃₂×C₁₀₇	C₂²	1	2	yes	—
8	C₂×#108×C₁₀₇	—	2	1	no	—
9	C₂×#108×C₁₀₇	C₂²	1	2	yes	—
10	C₂×#106×C₁₀₇	C₂²	1	1	yes	characteristic
11	#423×C₁₀₇	—	2	1	no	—
12	C₂×#102×C₁₀₇	—	2	1	no	—
13	C₂×#97×C₁₀₇	C₂²	1	1	yes	characteristic
14	#390×C₁₀₇	—	2	1	no	—
15	#361×C₁₀₇	—	2	4	no	—
16	C₂²×D₄×C₁₀₇	—	2	1	no	—
17	C₂×D₈×C₁₀₇	—	2	2	no	—
18	C₂×D₈×C₁₀₇	—	2	2	no	—
19	C₂×D₈×C₁₀₇	—	2	1	no	—
20	C₂×D₈×C₁₀₇	D₄	1	2	yes	—
21	C₂×M₁₆×C₁₀₇	—	2	2	no	—
22	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
25	C₂×C₂²⋊C₄×C₁₀₇	—	4	2	no	—
26	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
27	M₃₂×C₁₀₇	—	2	2	no	—
28	M₃₂×C₁₀₇	—	2	2	no	—
29	C₂×C₁₆×C₁₀₇	—	2	2	no	—
30	#108×C₁₀₇	—	2	2	no	—
31	#108×C₁₀₇	—	2	2	no	—
32	#108×C₁₀₇	—	4	2	no	—
33	#106×C₁₀₇	—	2	2	no	—
34	C₄⋊C₈×C₁₀₇	—	4	2	no	—
35	#102×C₁₀₇	—	4	2	no	—
36	#97×C₁₀₇	—	2	2	no	—
37	C₂⁴×C₁₀₇	—	4	1	no	—
38	C₂×D₄×C₁₀₇	—	2	2	no	—
39	C₂×D₄×C₁₀₇	—	4	1	no	—
40	C₂×D₄×C₁₀₇	—	4	1	no	—
41	C₂×D₄×C₁₀₇	—	4	1	no	—
42	C₂×D₄×C₁₀₇	—	4	1	no	—
43	C₂×D₄×C₁₀₇	—	4	1	no	—
44	C₂²×C₄×C₁₀₇	—	4	1	no	—
45	C₂²×C₄×C₁₀₇	SD₁₆	1	2	yes	—
46	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
47	D₈×C₁₀₇	—	2	4	no	—
48	D₈×C₁₀₇	—	4	2	no	—
49	M₁₆×C₁₀₇	—	4	2	no	—
50	M₁₆×C₁₀₇	—	4	2	no	—
51	C₂×C₈×C₁₀₇	—	2	1	no	—
52	C₂×C₈×C₁₀₇	—	2	1	no	—
53	C₂×C₈×C₁₀₇	—	4	2	no	—
54	C₂×C₈×C₁₀₇	D₈	1	2	yes	—
55	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₀₇	#41	1	2	yes	—
57	C₂×C₈×C₁₀₇	#41	1	2	yes	—
58	C₂×C₈×C₁₀₇	#41	1	1	yes	characteristic
59	C₄⋊C₄×C₁₀₇	—	4	1	no	—
60	C₄⋊C₄×C₁₀₇	—	4	1	no	—
61	C₂²⋊C₄×C₁₀₇	—	8	4	no	—
62	C₄²×C₁₀₇	—	2	1	no	—
63	C₄²×C₁₀₇	—	2	1	no	—
64	C₁₆×C₁₀₇	—	4	2	no	—
65	C₂³×C₁₀₇	—	4	2	no	—
66	C₂³×C₁₀₇	—	8	2	no	—
67	C₂³×C₁₀₇	—	8	2	no	—
68	C₂³×C₁₀₇	—	8	1	no	—
69	C₂³×C₁₀₇	—	8	1	no	—
70	C₂³×C₁₀₇	C₂×SD₁₆	1	1	yes	characteristic
71	D₄×C₁₀₇	—	4	2	no	—
72	D₄×C₁₀₇	—	4	2	no	—
73	D₄×C₁₀₇	—	8	1	no	—
74	D₄×C₁₀₇	—	8	1	no	—
75	C₂×C₄×C₁₀₇	—	2	2	no	—
76	C₂×C₄×C₁₀₇	—	4	2	no	—
77	C₂×C₄×C₁₀₇	—	8	2	no	—
78	C₂×C₄×C₁₀₇	—	8	1	no	—
79	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
80	C₂×C₄×C₁₀₇	#123	1	1	yes	characteristic
81	C₂×C₄×C₁₀₇	#124	1	1	yes	characteristic
82	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	1	yes	characteristic
84	C₂×C₄×C₁₀₇	#137	1	1	yes	characteristic
85	C₈×C₁₀₇	—	2	2	no	—
86	C₈×C₁₀₇	—	8	2	no	—
87	C₈×C₁₀₇	#123	1	2	yes	—
88	C₈×C₁₀₇	#126	1	2	yes	—
89	C₂²×C₁₀₇	—	2	2	no	—
90	C₂²×C₁₀₇	—	8	4	no	—
91	C₂²×C₁₀₇	—	8	2	no	—
92	C₂²×C₁₀₇	—	16	1	no	—
93	C₂²×C₁₀₇	—	16	1	no	—
94	C₂²×C₁₀₇	—	16	2	no	—
95	C₂²×C₁₀₇	#461	1	1	yes	characteristic
96	C₂²×C₁₀₇	#481	1	1	yes	characteristic
97	C₂²×C₁₀₇	#486	1	1	yes	characteristic
98	C₄×C₁₀₇	—	4	2	no	—
99	C₄×C₁₀₇	—	16	1	no	—
100	C₄×C₁₀₇	#397	1	1	yes	characteristic
101	C₄×C₁₀₇	#459	1	1	yes	characteristic
102	C₄×C₁₀₇	#480	1	1	yes	characteristic
103	C₄×C₁₀₇	#489	1	1	yes	characteristic
104	#13487	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂×C₁₀₇	—	2	1	no	—
106	C₂×C₁₀₇	—	2	1	no	—
107	C₂×C₁₀₇	—	16	2	no	—
108	C₂×C₁₀₇	#2071	1	1	yes	characteristic
109	C₂×C₁₀₇	#2238	1	2	yes	—
110	C₂×#361	C₂×C₁₀₇	1	2	yes	—
111	#1972	C₂×C₁₀₇	1	1	yes	characteristic
112	#1849	C₂×C₁₀₇	1	1	yes	characteristic, complemented
113	#1383	C₂×C₁₀₇	1	2	yes	complemented
114	#1377	C₂×C₁₀₇	1	1	yes	characteristic, complemented
115	C₁₀₇	#13487	1	1	yes	characteristic, direct product factor, Sylow
116	C₂²×D₈	C₂²×C₁₀₇	1	1	yes	characteristic
117	C₂×M₃₂	C₂²×C₁₀₇	1	2	yes	—
118	C₂×#108	—	2	1	no	—
119	C₂×#108	C₂²×C₁₀₇	1	2	yes	—
120	C₂×#106	C₂²×C₁₀₇	1	1	yes	characteristic
121	#423	—	2	1	no	—
122	C₂×#102	—	2	1	no	—
123	C₂×#97	C₂²×C₁₀₇	1	1	yes	characteristic
124	#390	—	2	1	no	—
125	#361	—	2	4	no	—
126	C₂²×D₄	—	2	1	no	—
127	C₂×D₈	—	2	2	no	—
128	C₂×D₈	—	2	2	no	—
129	C₂×D₈	—	2	1	no	—
130	C₂×D₈	D₄×C₁₀₇	1	2	yes	—
131	C₂×M₁₆	—	2	2	no	—
132	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
133	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
134	C₂×C₄⋊C₄	—	2	1	no	—
135	C₂×C₂²⋊C₄	—	4	2	no	—
136	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
137	M₃₂	—	2	2	no	—
138	M₃₂	—	2	2	no	—
139	C₂×C₁₆	—	2	2	no	—
140	#108	—	2	2	no	—
141	#108	—	2	2	no	—
142	#108	—	4	2	no	—
143	#106	—	2	2	no	—
144	C₄⋊C₈	—	4	2	no	—
145	#102	—	4	2	no	—
146	#97	—	2	2	no	—
147	C₂⁴	—	4	1	no	—
148	C₂×D₄	—	2	2	no	—
149	C₂×D₄	—	4	1	no	—
150	C₂×D₄	—	4	1	no	—
151	C₂×D₄	—	4	1	no	—
152	C₂×D₄	—	4	1	no	—
153	C₂×D₄	—	4	1	no	—
154	C₂²×C₄	—	4	1	no	—
155	C₂²×C₄	SD₁₆×C₁₀₇	1	2	yes	—
156	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
157	D₈	—	2	4	no	—
158	D₈	—	4	2	no	—
159	M₁₆	—	4	2	no	—
160	M₁₆	—	4	2	no	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	4	2	no	—
164	C₂×C₈	D₈×C₁₀₇	1	2	yes	—
165	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
166	C₂×C₈	#41×C₁₀₇	1	2	yes	—
167	C₂×C₈	#41×C₁₀₇	1	2	yes	—
168	C₂×C₈	#41×C₁₀₇	1	1	yes	characteristic
169	C₄⋊C₄	—	4	1	no	—
170	C₄⋊C₄	—	4	1	no	—
171	C₂²⋊C₄	—	8	4	no	—
172	C₄²	—	2	1	no	—
173	C₄²	—	2	1	no	—
174	C₁₆	—	4	2	no	—
175	C₂³	—	4	2	no	—
176	C₂³	—	8	2	no	—
177	C₂³	—	8	2	no	—
178	C₂³	—	8	1	no	—
179	C₂³	—	8	1	no	—
180	C₂³	C₂×SD₁₆×C₁₀₇	1	1	yes	characteristic
181	D₄	—	4	2	no	—
182	D₄	—	4	2	no	—
183	D₄	—	8	1	no	—
184	D₄	—	8	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	8	2	no	—
188	C₂×C₄	—	8	1	no	—
189	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
190	C₂×C₄	#123×C₁₀₇	1	1	yes	characteristic
191	C₂×C₄	#124×C₁₀₇	1	1	yes	characteristic
192	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
193	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
194	C₂×C₄	#137×C₁₀₇	1	1	yes	characteristic
195	C₈	—	2	2	no	—
196	C₈	—	8	2	no	—
197	C₈	#123×C₁₀₇	1	2	yes	—
198	C₈	#126×C₁₀₇	1	2	yes	—
199	C₂²	—	2	2	no	—
200	C₂²	—	8	4	no	—
201	C₂²	—	8	2	no	—
202	C₂²	—	16	1	no	—
203	C₂²	—	16	1	no	—
204	C₂²	—	16	2	no	—
205	C₂²	#461×C₁₀₇	1	1	yes	characteristic
206	C₂²	#481×C₁₀₇	1	1	yes	characteristic
207	C₂²	#486×C₁₀₇	1	1	yes	characteristic
208	C₄	—	4	2	no	—
209	C₄	—	16	1	no	—
210	C₄	#397×C₁₀₇	1	1	yes	characteristic
211	C₄	#459×C₁₀₇	1	1	yes	characteristic
212	C₄	#480×C₁₀₇	1	1	yes	characteristic
213	C₄	#489×C₁₀₇	1	1	yes	characteristic
214	C₂	—	2	1	no	—
215	C₂	—	2	1	no	—
216	C₂	—	16	2	no	—
217	C₂	C₁₀₇×#2071	1	1	yes	characteristic
218	C₂	C₁₀₇×#2238	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#361×C₁₀₇

C₂

yes

maximal

C₁₀₇×#1972

C₂

yes

maximal, characteristic

C₁₀₇×#1849

C₂

yes

maximal, characteristic, complemented

C₁₀₇×#1383

C₂

yes

maximal, complemented

C₁₀₇×#1377

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₁₀₇

C₂²

yes

characteristic

C₂×M₃₂×C₁₀₇

C₂²

yes

—

C₂×#108×C₁₀₇

—

C₂×#108×C₁₀₇

C₂²

yes

—

C₂×#106×C₁₀₇

C₂²

yes

characteristic

#423×C₁₀₇

—

C₂×#102×C₁₀₇

—

C₂×#97×C₁₀₇

C₂²

yes

characteristic

#390×C₁₀₇

—

#361×C₁₀₇

—

C₂²×D₄×C₁₀₇

—

C₂×D₈×C₁₀₇

—

C₂×D₈×C₁₀₇

—

C₂×D₈×C₁₀₇

—

C₂×D₈×C₁₀₇

D₄

yes

—

C₂×M₁₆×C₁₀₇

—

C₂²×C₈×C₁₀₇

D₄

yes

characteristic

C₂²×C₈×C₁₀₇

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₁₀₇

—

C₂×C₂²⋊C₄×C₁₀₇

—

C₂×C₄²×C₁₀₇

D₄

yes

characteristic

M₃₂×C₁₀₇

—

M₃₂×C₁₀₇

—

C₂×C₁₆×C₁₀₇

—

#108×C₁₀₇

—

#108×C₁₀₇

—

#108×C₁₀₇

—

#106×C₁₀₇

—

C₄⋊C₈×C₁₀₇

—

#102×C₁₀₇

—

#97×C₁₀₇

—

C₂⁴×C₁₀₇

—

C₂×D₄×C₁₀₇

—

C₂×D₄×C₁₀₇

—

C₂×D₄×C₁₀₇

—

C₂×D₄×C₁₀₇

—

C₂×D₄×C₁₀₇

—

C₂×D₄×C₁₀₇

—

C₂²×C₄×C₁₀₇

—

C₂²×C₄×C₁₀₇

SD₁₆

yes

—

C₂²×C₄×C₁₀₇

C₂×D₄

yes

characteristic

D₈×C₁₀₇

—

D₈×C₁₀₇

—

M₁₆×C₁₀₇

—

M₁₆×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

D₈

yes

—

C₂×C₈×C₁₀₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₀₇

#41

yes

—

C₂×C₈×C₁₀₇

#41

yes

—

C₂×C₈×C₁₀₇

#41

yes

characteristic

C₄⋊C₄×C₁₀₇

—

C₄⋊C₄×C₁₀₇

—

C₂²⋊C₄×C₁₀₇

—

C₄²×C₁₀₇

—

C₄²×C₁₀₇

—

C₁₆×C₁₀₇

—

C₂³×C₁₀₇

—

C₂³×C₁₀₇

—

C₂³×C₁₀₇

—

C₂³×C₁₀₇

—

C₂³×C₁₀₇

—

C₂³×C₁₀₇

C₂×SD₁₆

yes

characteristic

D₄×C₁₀₇

—

D₄×C₁₀₇

—

D₄×C₁₀₇

—

D₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

yes

C₂×C₄×C₁₀₇

yes

C₂×C₄×C₁₀₇

yes

C₂×C₄×C₁₀₇

C₂×D₈

yes

C₂×C₄×C₁₀₇

yes

C₂×C₄×C₁₀₇

yes

C₈×C₁₀₇

—

C₈×C₁₀₇

—

C₈×C₁₀₇

#123

yes

—

C₈×C₁₀₇

#126

yes

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

yes

C₂²×C₁₀₇

yes

C₂²×C₁₀₇

yes

C₄×C₁₀₇

—

C₄×C₁₀₇

—

100

C₄×C₁₀₇

#397

yes

characteristic

101

C₄×C₁₀₇

#459

yes

characteristic

102

C₄×C₁₀₇

#480

yes

characteristic

103

C₄×C₁₀₇

#489

yes

characteristic

104

#13487

C₁₀₇

yes

maximal, characteristic, direct product factor, Sylow

105

C₂×C₁₀₇

—

106

C₂×C₁₀₇

—

107

C₂×C₁₀₇

—

108

C₂×C₁₀₇

#2071

yes

characteristic

109

C₂×C₁₀₇

#2238

yes

—

110

C₂×#361

C₂×C₁₀₇

yes

—

111

#1972

C₂×C₁₀₇

yes

characteristic

112

#1849

C₂×C₁₀₇

yes

characteristic, complemented

113

#1383

C₂×C₁₀₇

yes

complemented

114

#1377

C₂×C₁₀₇

yes

characteristic, complemented

115

C₁₀₇

#13487

yes

characteristic, direct product factor, Sylow

116

C₂²×D₈

C₂²×C₁₀₇

yes

characteristic

117

C₂×M₃₂

C₂²×C₁₀₇

yes

—

118

C₂×#108

—

119

C₂×#108

C₂²×C₁₀₇

yes

—

120

C₂×#106

C₂²×C₁₀₇

yes

characteristic

121

#423

—

122

C₂×#102

—

123

C₂×#97

C₂²×C₁₀₇

yes

characteristic

124

#390

—

125

#361

—

126

C₂²×D₄

—

127

C₂×D₈

—

128

C₂×D₈

—

129

C₂×D₈

—

130

C₂×D₈

D₄×C₁₀₇

yes

—

131

C₂×M₁₆

—

132

C₂²×C₈

D₄×C₁₀₇

yes

characteristic

133

C₂²×C₈

C₂³×C₁₀₇

yes

characteristic

134

C₂×C₄⋊C₄

—

135

C₂×C₂²⋊C₄

—

136

C₂×C₄²

D₄×C₁₀₇

yes

characteristic

137

M₃₂

—

138

M₃₂

—

139

C₂×C₁₆

—

140

#108

—

141

#108

—

142

#108

—

143

#106

—

144

C₄⋊C₈

—

145

#102

—

146

#97

—

147

C₂⁴

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂²×C₄

—

155

C₂²×C₄

SD₁₆×C₁₀₇

yes

—

156

C₂²×C₄

C₂×D₄×C₁₀₇

yes

characteristic

157

D₈

—

158

D₈

—

159

M₁₆

—

160

M₁₆

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

D₈×C₁₀₇

yes

—

165

C₂×C₈

C₂×D₄×C₁₀₇

yes

characteristic

166

C₂×C₈

#41×C₁₀₇

yes

—

167

C₂×C₈

#41×C₁₀₇

yes

—

168

C₂×C₈

#41×C₁₀₇

yes

characteristic

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₂²⋊C₄

—

172

C₄²

—

173

C₄²

—

174

C₁₆

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

C₂×SD₁₆×C₁₀₇

yes

characteristic

181

D₄

—

182

D₄

—

183

D₄

—

184

D₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

#121×C₁₀₇

yes

characteristic

190

C₂×C₄

#123×C₁₀₇

yes

characteristic

191

C₂×C₄

#124×C₁₀₇

yes

characteristic

192

C₂×C₄

C₂×D₈×C₁₀₇

yes

characteristic

193

C₂×C₄

AGL(1,ℤ/8)×C₁₀₇

yes

characteristic

194

C₂×C₄

#137×C₁₀₇

yes

characteristic

195

C₈

—

196

C₈

—

197

C₈

#123×C₁₀₇

yes

—

198

C₈

#126×C₁₀₇

yes

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

#461×C₁₀₇

yes

characteristic

206

C₂²

#481×C₁₀₇

yes

characteristic

207

C₂²

#486×C₁₀₇

yes

characteristic

208

C₄

—

209

C₄

—

210

C₄

#397×C₁₀₇

yes

characteristic

211

C₄

#459×C₁₀₇

yes

characteristic

212

C₄

#480×C₁₀₇

yes

characteristic

213

C₄

#489×C₁₀₇

yes

characteristic

214

C₂

—

215

C₂

—

216

C₂

—

217

C₂

C₁₀₇×#2071

yes

characteristic

218

C₂

C₁₀₇×#2238

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₀₇	#481
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₀₇
prime radical	C₂²×D₈×C₁₀₇	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂²×C₄×C₁₀₇ ◁ C₂×#97×C₁₀₇ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₀₇

#481

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₀₇

prime radical

C₂²×D₈×C₁₀₇

C₂²

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₀₇ ◁ C₂²×C₄×C₁₀₇ ◁ C₂×#97×C₁₀₇ ◁ G

N	H ≅ G/N	type
3. C₁₀₇×#1849	C₂	semidirect
4. C₁₀₇×#1383	C₂	semidirect
5. C₁₀₇×#1377	C₂	semidirect
104. #13487	C₁₀₇	direct (N × H)
112. #1849	C₂×C₁₀₇	semidirect
113. #1383	C₂×C₁₀₇	semidirect
114. #1377	C₂×C₁₀₇	semidirect
115. C₁₀₇	#13487	direct (N × H)

H ≅ G/N

type

3. C₁₀₇×#1849

C₂

semidirect

4. C₁₀₇×#1383

C₂

semidirect

5. C₁₀₇×#1377

C₂

semidirect

104. #13487

C₁₀₇

direct (N × H)

112. #1849

C₂×C₁₀₇

semidirect

113. #1383

C₂×C₁₀₇

semidirect

114. #1377

C₂×C₁₀₇

semidirect

115. C₁₀₇

#13487

direct (N × H)

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

subgroup	index
C₂×#361×C₁₀₇	2
C₁₀₇×#1972	2
C₁₀₇×#1849	2
C₁₀₇×#1383	2
C₁₀₇×#1377	2
#13487	107

subgroup

index

C₂×#361×C₁₀₇

C₁₀₇×#1972

C₁₀₇×#1849

C₁₀₇×#1383

C₁₀₇×#1377

#13487

107

Subgroups — C₁₀₇×#13487 #41039451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C107×#13487 #41039451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#13487 #41039451