Group #41034602 — subgroups

Subgroups — C₁₀₇×#8638 #41034602

Order 27392.

404 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 138 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	C₁₀₇×#2931	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇×#1567	C₂	1	2	yes	maximal, complemented
3	C₁₀₇×#1560	C₂	1	2	yes	maximal
4	C₁₀₇×#1309	C₂	1	2	yes	maximal, complemented
5	C₂×#131×C₁₀₇	C₄	1	2	yes	—
6	#532×C₁₀₇	C₂²	1	1	yes	characteristic
7	#436×C₁₀₇	—	2	2	no	—
8	C₈×D₄×C₁₀₇	—	2	2	no	—
9	#423×C₁₀₇	C₂²	1	4	yes	—
10	#423×C₁₀₇	C₂²	1	1	yes	characteristic
11	#408×C₁₀₇	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
13	#335×C₁₀₇	—	2	2	no	—
14	#335×C₁₀₇	—	2	2	no	—
15	#333×C₁₀₇	—	2	2	no	—
16	#331×C₁₀₇	—	2	2	no	—
17	C₂×#41×C₁₀₇	C₂×C₄	1	2	yes	—
18	#131×C₁₀₇	—	4	4	no	—
19	C₂×M₁₆×C₁₀₇	—	2	2	no	—
20	C₂×M₁₆×C₁₀₇	—	2	4	no	—
21	C₂×M₁₆×C₁₀₇	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₁₀₇	—	2	2	no	—
23	C₂²×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
25	C₄⋊Q₈×C₁₀₇	D₄	1	1	yes	characteristic
26	#127×C₁₀₇	D₄	1	1	yes	characteristic
27	#124×C₁₀₇	Q₈	1	2	yes	—
28	#121×C₁₀₇	—	2	2	no	—
29	C₄×D₄×C₁₀₇	—	2	2	no	—
30	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
31	C₄⋊C₈×C₁₀₇	—	2	2	no	—
32	C₄⋊C₈×C₁₀₇	—	2	4	no	—
33	C₄⋊C₈×C₁₀₇	—	2	4	no	—
34	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
35	C₄×C₈×C₁₀₇	D₄	1	2	yes	—
36	C₄×C₈×C₁₀₇	D₄	1	2	yes	—
37	#41×C₁₀₇	—	4	2	no	—
38	#41×C₁₀₇	—	4	2	no	—
39	C₂×Q₈×C₁₀₇	C₄⋊C₄	1	2	yes	—
40	C₂×D₄×C₁₀₇	—	2	2	no	—
41	C₂×D₄×C₁₀₇	—	2	2	no	—
42	C₂×D₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
43	C₂²×C₄×C₁₀₇	—	2	2	no	—
44	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
46	M₁₆×C₁₀₇	—	4	4	no	—
47	M₁₆×C₁₀₇	—	4	2	no	—
48	M₁₆×C₁₀₇	—	8	4	no	—
49	C₂×C₈×C₁₀₇	—	2	2	no	—
50	C₂×C₈×C₁₀₇	—	2	2	no	—
51	C₂×C₈×C₁₀₇	—	4	1	no	—
52	C₂×C₈×C₁₀₇	—	4	4	no	—
53	C₂×C₈×C₁₀₇	—	4	4	no	—
54	C₂×C₈×C₁₀₇	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
57	C₄⋊C₄×C₁₀₇	—	2	2	no	—
58	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
59	C₄²×C₁₀₇	C₂×D₄	1	2	yes	—
60	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
62	C₂³×C₁₀₇	—	2	2	no	—
63	C₂³×C₁₀₇	#117	1	1	yes	characteristic
64	Q₈×C₁₀₇	—	4	2	no	—
65	D₄×C₁₀₇	—	4	2	no	—
66	D₄×C₁₀₇	—	4	4	no	—
67	D₄×C₁₀₇	—	4	2	no	—
68	D₄×C₁₀₇	—	4	2	no	—
69	C₂×C₄×C₁₀₇	—	2	1	no	—
70	C₂×C₄×C₁₀₇	—	2	1	no	—
71	C₂×C₄×C₁₀₇	—	2	2	no	—
72	C₂×C₄×C₁₀₇	—	2	2	no	—
73	C₂×C₄×C₁₀₇	—	2	2	no	—
74	C₂×C₄×C₁₀₇	—	4	2	no	—
75	C₂×C₄×C₁₀₇	—	4	2	no	—
76	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₀₇	#121	1	2	yes	—
79	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
80	C₈×C₁₀₇	—	2	1	no	—
81	C₈×C₁₀₇	—	2	2	no	—
82	C₈×C₁₀₇	—	4	2	no	—
83	C₈×C₁₀₇	—	8	4	no	—
84	C₈×C₁₀₇	#100	1	2	yes	—
85	C₂²×C₁₀₇	—	2	1	no	—
86	C₂²×C₁₀₇	—	2	2	no	—
87	C₂²×C₁₀₇	—	4	2	no	—
88	C₂²×C₁₀₇	—	4	4	no	—
89	C₂²×C₁₀₇	#380	1	1	yes	characteristic
90	C₄×C₁₀₇	—	2	1	no	—
91	C₄×C₁₀₇	—	2	2	no	—
92	C₄×C₁₀₇	—	4	2	no	—
93	C₄×C₁₀₇	C₂×#100	1	1	yes	characteristic
94	C₄×C₁₀₇	#413	1	1	yes	characteristic
95	C₄×C₁₀₇	#472	1	2	yes	—
96	C₄×C₁₀₇	#473	1	2	yes	—
97	#8638	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂×C₁₀₇	—	4	1	no	—
99	C₂×C₁₀₇	—	8	2	no	—
100	C₂×C₁₀₇	#1800	1	1	yes	characteristic
101	C₂×C₁₀₇	#1816	1	2	yes	—
102	#2931	C₂×C₁₀₇	1	1	yes	characteristic
103	#1567	C₂×C₁₀₇	1	2	yes	complemented
104	#1560	C₂×C₁₀₇	1	2	yes	—
105	#1309	C₂×C₁₀₇	1	2	yes	complemented
106	C₁₀₇	#8638	1	1	yes	characteristic, direct product factor, Sylow
107	C₂×#131	C₄×C₁₀₇	1	2	yes	—
108	#532	C₂²×C₁₀₇	1	1	yes	characteristic
109	#436	—	2	2	no	—
110	C₈×D₄	—	2	2	no	—
111	#423	C₂²×C₁₀₇	1	4	yes	—
112	#423	C₂²×C₁₀₇	1	1	yes	characteristic
113	#408	C₄×C₁₀₇	1	2	yes	—
114	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
115	#335	—	2	2	no	—
116	#335	—	2	2	no	—
117	#333	—	2	2	no	—
118	#331	—	2	2	no	—
119	C₂×#41	C₂×C₄×C₁₀₇	1	2	yes	—
120	#131	—	4	4	no	—
121	C₂×M₁₆	—	2	2	no	—
122	C₂×M₁₆	—	2	4	no	—
123	C₂×M₁₆	C₂×C₄×C₁₀₇	1	2	yes	—
124	C₂²×C₈	—	2	2	no	—
125	C₂²×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
126	C₂²×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
127	C₄⋊Q₈	D₄×C₁₀₇	1	1	yes	characteristic
128	#127	D₄×C₁₀₇	1	1	yes	characteristic
129	#124	Q₈×C₁₀₇	1	2	yes	—
130	#121	—	2	2	no	—
131	C₄×D₄	—	2	2	no	—
132	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
133	C₄⋊C₈	—	2	2	no	—
134	C₄⋊C₈	—	2	4	no	—
135	C₄⋊C₈	—	2	4	no	—
136	C₂²⋊C₈	—	2	4	no	—
137	C₄×C₈	D₄×C₁₀₇	1	2	yes	—
138	C₄×C₈	D₄×C₁₀₇	1	2	yes	—
139	#41	—	4	2	no	—
140	#41	—	4	2	no	—
141	C₂×Q₈	C₄⋊C₄×C₁₀₇	1	2	yes	—
142	C₂×D₄	—	2	2	no	—
143	C₂×D₄	—	2	2	no	—
144	C₂×D₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
147	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
148	M₁₆	—	4	4	no	—
149	M₁₆	—	4	2	no	—
150	M₁₆	—	8	4	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	—	4	1	no	—
154	C₂×C₈	—	4	4	no	—
155	C₂×C₈	—	4	4	no	—
156	C₂×C₈	C₂²⋊C₄×C₁₀₇	1	2	yes	—
157	C₂×C₈	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
158	C₂×C₈	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
159	C₄⋊C₄	—	2	2	no	—
160	C₂²⋊C₄	—	2	4	no	—
161	C₄²	C₂×D₄×C₁₀₇	1	2	yes	—
162	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
163	C₄²	C₂×Q₈×C₁₀₇	1	1	yes	characteristic
164	C₂³	—	2	2	no	—
165	C₂³	#117×C₁₀₇	1	1	yes	characteristic
166	Q₈	—	4	2	no	—
167	D₄	—	4	2	no	—
168	D₄	—	4	4	no	—
169	D₄	—	4	2	no	—
170	D₄	—	4	2	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	4	2	no	—
177	C₂×C₄	—	4	2	no	—
178	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
179	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
180	C₂×C₄	#121×C₁₀₇	1	2	yes	—
181	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
182	C₈	—	2	1	no	—
183	C₈	—	2	2	no	—
184	C₈	—	4	2	no	—
185	C₈	—	8	4	no	—
186	C₈	#100×C₁₀₇	1	2	yes	—
187	C₂²	—	2	1	no	—
188	C₂²	—	2	2	no	—
189	C₂²	—	4	2	no	—
190	C₂²	—	4	4	no	—
191	C₂²	#380×C₁₀₇	1	1	yes	characteristic
192	C₄	—	2	1	no	—
193	C₄	—	2	2	no	—
194	C₄	—	4	2	no	—
195	C₄	C₂×#100×C₁₀₇	1	1	yes	characteristic
196	C₄	#413×C₁₀₇	1	1	yes	characteristic
197	C₄	#472×C₁₀₇	1	2	yes	—
198	C₄	#473×C₁₀₇	1	2	yes	—
199	C₂	—	4	1	no	—
200	C₂	—	8	2	no	—
201	C₂	C₁₀₇×#1800	1	1	yes	characteristic
202	C₂	C₁₀₇×#1816	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₀₇×#2931

C₂

yes

maximal, characteristic

C₁₀₇×#1567

C₂

yes

maximal, complemented

C₁₀₇×#1560

C₂

yes

maximal

C₁₀₇×#1309

C₂

yes

maximal, complemented

C₂×#131×C₁₀₇

C₄

yes

—

#532×C₁₀₇

C₂²

yes

characteristic

#436×C₁₀₇

—

C₈×D₄×C₁₀₇

—

#423×C₁₀₇

C₂²

yes

—

#423×C₁₀₇

C₂²

yes

characteristic

#408×C₁₀₇

C₄

yes

—

C₂×C₄×C₈×C₁₀₇

C₂²

yes

characteristic

#335×C₁₀₇

—

#335×C₁₀₇

—

#333×C₁₀₇

—

#331×C₁₀₇

—

C₂×#41×C₁₀₇

C₂×C₄

yes

—

#131×C₁₀₇

—

C₂×M₁₆×C₁₀₇

—

C₂×M₁₆×C₁₀₇

—

C₂×M₁₆×C₁₀₇

C₂×C₄

yes

—

C₂²×C₈×C₁₀₇

—

C₂²×C₈×C₁₀₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₀₇

C₂×C₄

yes

characteristic

C₄⋊Q₈×C₁₀₇

D₄

yes

characteristic

#127×C₁₀₇

D₄

yes

characteristic

#124×C₁₀₇

Q₈

yes

—

#121×C₁₀₇

—

C₄×D₄×C₁₀₇

—

C₂×C₄²×C₁₀₇

C₂³

yes

characteristic

C₄⋊C₈×C₁₀₇

—

C₄⋊C₈×C₁₀₇

—

C₄⋊C₈×C₁₀₇

—

C₂²⋊C₈×C₁₀₇

—

C₄×C₈×C₁₀₇

D₄

yes

—

C₄×C₈×C₁₀₇

D₄

yes

—

#41×C₁₀₇

—

#41×C₁₀₇

—

C₂×Q₈×C₁₀₇

C₄⋊C₄

yes

—

C₂×D₄×C₁₀₇

—

C₂×D₄×C₁₀₇

—

C₂×D₄×C₁₀₇

C₄⋊C₄

yes

—

C₂²×C₄×C₁₀₇

—

C₂²×C₄×C₁₀₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₀₇

#41

yes

—

M₁₆×C₁₀₇

—

M₁₆×C₁₀₇

—

M₁₆×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

C₂²⋊C₄

yes

—

C₂×C₈×C₁₀₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₀₇

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₀₇

—

C₂²⋊C₄×C₁₀₇

—

C₄²×C₁₀₇

C₂×D₄

yes

—

C₄²×C₁₀₇

C₂×D₄

yes

characteristic

C₄²×C₁₀₇

C₂×Q₈

yes

characteristic

C₂³×C₁₀₇

—

C₂³×C₁₀₇

#117

yes

characteristic

Q₈×C₁₀₇

—

D₄×C₁₀₇

—

D₄×C₁₀₇

—

D₄×C₁₀₇

—

D₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₀₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₀₇

#121

yes

—

C₂×C₄×C₁₀₇

C₂²⋊Q₈

yes

—

C₈×C₁₀₇

—

C₈×C₁₀₇

—

C₈×C₁₀₇

—

C₈×C₁₀₇

—

C₈×C₁₀₇

#100

yes

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

#380

yes

characteristic

C₄×C₁₀₇

—

C₄×C₁₀₇

—

C₄×C₁₀₇

—

C₄×C₁₀₇

yes

C₄×C₁₀₇

yes

C₄×C₁₀₇

yes

—

C₄×C₁₀₇

#473

yes

—

#8638

C₁₀₇

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₁₀₇

—

C₂×C₁₀₇

—

100

C₂×C₁₀₇

#1800

yes

characteristic

101

C₂×C₁₀₇

#1816

yes

—

102

#2931

C₂×C₁₀₇

yes

characteristic

103

#1567

C₂×C₁₀₇

yes

complemented

104

#1560

C₂×C₁₀₇

yes

—

105

#1309

C₂×C₁₀₇

yes

complemented

106

C₁₀₇

#8638

yes

characteristic, direct product factor, Sylow

107

C₂×#131

C₄×C₁₀₇

yes

—

108

#532

C₂²×C₁₀₇

yes

characteristic

109

#436

—

110

C₈×D₄

—

111

#423

C₂²×C₁₀₇

yes

—

112

#423

C₂²×C₁₀₇

yes

characteristic

113

#408

C₄×C₁₀₇

yes

—

114

C₂×C₄×C₈

C₂²×C₁₀₇

yes

characteristic

115

#335

—

116

#335

—

117

#333

—

118

#331

—

119

C₂×#41

C₂×C₄×C₁₀₇

yes

—

120

#131

—

121

C₂×M₁₆

—

122

C₂×M₁₆

—

123

C₂×M₁₆

C₂×C₄×C₁₀₇

yes

—

124

C₂²×C₈

—

125

C₂²×C₈

C₂×C₄×C₁₀₇

yes

characteristic

126

C₂²×C₈

C₂×C₄×C₁₀₇

yes

characteristic

127

C₄⋊Q₈

D₄×C₁₀₇

yes

characteristic

128

#127

D₄×C₁₀₇

yes

characteristic

129

#124

Q₈×C₁₀₇

yes

—

130

#121

—

131

C₄×D₄

—

132

C₂×C₄²

C₂³×C₁₀₇

yes

characteristic

133

C₄⋊C₈

—

134

C₄⋊C₈

—

135

C₄⋊C₈

—

136

C₂²⋊C₈

—

137

C₄×C₈

D₄×C₁₀₇

yes

—

138

C₄×C₈

D₄×C₁₀₇

yes

—

139

#41

—

140

#41

—

141

C₂×Q₈

C₄⋊C₄×C₁₀₇

yes

—

142

C₂×D₄

—

143

C₂×D₄

—

144

C₂×D₄

C₄⋊C₄×C₁₀₇

yes

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂²×C₄×C₁₀₇

yes

characteristic

147

C₂²×C₄

#41×C₁₀₇

yes

—

148

M₁₆

—

149

M₁₆

—

150

M₁₆

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

C₂²⋊C₄×C₁₀₇

yes

—

157

C₂×C₈

C₂²⋊C₄×C₁₀₇

yes

characteristic

158

C₂×C₈

C₂²⋊C₄×C₁₀₇

yes

characteristic

159

C₄⋊C₄

—

160

C₂²⋊C₄

—

161

C₄²

C₂×D₄×C₁₀₇

yes

—

162

C₄²

C₂×D₄×C₁₀₇

yes

characteristic

163

C₄²

C₂×Q₈×C₁₀₇

yes

characteristic

164

C₂³

—

165

C₂³

#117×C₁₀₇

yes

characteristic

166

Q₈

—

167

D₄

—

168

D₄

—

169

D₄

—

170

D₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

C₂×C₂²⋊C₄×C₁₀₇

yes

characteristic

179

C₂×C₄

C₂×C₄⋊C₄×C₁₀₇

yes

characteristic

180

C₂×C₄

#121×C₁₀₇

yes

—

181

C₂×C₄

C₂²⋊Q₈×C₁₀₇

yes

—

182

C₈

—

183

C₈

—

184

C₈

—

185

C₈

—

186

C₈

#100×C₁₀₇

yes

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

#380×C₁₀₇

yes

characteristic

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

C₂×#100×C₁₀₇

yes

characteristic

196

C₄

#413×C₁₀₇

yes

characteristic

197

C₄

#472×C₁₀₇

yes

—

198

C₄

#473×C₁₀₇

yes

—

199

C₂

—

200

C₂

—

201

C₂

C₁₀₇×#1800

yes

characteristic

202

C₂

C₁₀₇×#1816

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₀₇	#380
commutator	C₂²×C₄	C₂²×C₄×C₁₀₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₇
prime radical	#532×C₁₀₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂×C₄²×C₁₀₇ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₀₇

#380

commutator

C₂²×C₄

C₂²×C₄×C₁₀₇

Frattini, cosocle

C₂×C₄²

C₂³×C₁₀₇

prime radical

#532×C₁₀₇

C₂²

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₀₇ ◁ C₂×C₄²×C₁₀₇ ◁ G

N	H ≅ G/N	type
2. C₁₀₇×#1567	C₂	semidirect
4. C₁₀₇×#1309	C₂	semidirect
97. #8638	C₁₀₇	direct (N × H)
103. #1567	C₂×C₁₀₇	semidirect
105. #1309	C₂×C₁₀₇	semidirect
106. C₁₀₇	#8638	direct (N × H)

H ≅ G/N

type

2. C₁₀₇×#1567

C₂

semidirect

4. C₁₀₇×#1309

C₂

semidirect

97. #8638

C₁₀₇

direct (N × H)

103. #1567

C₂×C₁₀₇

semidirect

105. #1309

C₂×C₁₀₇

semidirect

106. C₁₀₇

#8638

direct (N × H)

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

subgroup	index
C₁₀₇×#2931	2
C₁₀₇×#1567	2
C₁₀₇×#1560	2
C₁₀₇×#1309	2
#8638	107

subgroup

index

C₁₀₇×#2931

C₁₀₇×#1567

C₁₀₇×#1560

C₁₀₇×#1309

#8638

107

Subgroups — C₁₀₇×#8638 #41034602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C107×#8638 #41034602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#8638 #41034602