Finite Group Databasebeta

← C107×#7521 #41033485

Subgroups — C107×#7521 #41033485

Order 27392.

148 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#1634C211yesmaximal, characteristic
2C107×#1411C211yesmaximal, characteristic, complemented
3C107×#1358C211yesmaximal, characteristic, complemented
4#555×C107C411yescharacteristic
5#494×C107C2211yescharacteristic
6#476×C107—21no—
7#364×C107—21no—
8#356×C107—21no—
9#333×C107C411yescharacteristic
10D4⋊C8×C107—21no—
11C2×Q16×C107—41no—
12C4⋊Q8×C107C2×C411yescharacteristic
13C4⋊Q8×C107D411yescharacteristic
14#124×C107—41no—
15#121×C107—41no—
16C4×D4×C107—21no—
17#117×C107—41no—
18M32×C107—41no—
19#106×C107—41no—
20C4⋊C8×C107—21no—
21#102×C107—41no—
22#101×C107—41no—
23C4×C8×C107D411yescharacteristic
24C2×Q8×C107—21no—
25C2×Q8×C107—21no—
26C2×D4×C107—21no—
27C2×D4×C107—41no—
28C22×C4×C107—41no—
29Q16×C107—81no—
30Q16×C107—81no—
31M16×C107—81no—
32C2×C8×C107—21no—
33C2×C8×C107—41no—
34C4⋊C4×C107—21no—
35C4⋊C4×C107—41no—
36C4⋊C4×C107—41no—
37C22⋊C4×C107—42no—
38C22⋊C4×C107—41no—
39C42×C107—41no—
40C42×C107C22⋊C411yescharacteristic
41C16×C107—81no—
42C23×C107—41no—
43Q8×C107—81no—
44Q8×C107—81no—
45D4×C107—41no—
46D4×C107—41no—
47D4×C107—161no—
48C2×C4×C107—21no—
49C2×C4×C107—41no—
50C2×C4×C107—41no—
51C2×C4×C107—41no—
52C2×C4×C107—81no—
53C2×C4×C107—81no—
54C2×C4×C107#9911yescharacteristic
55C8×C107—21no—
56C8×C107—21no—
57C8×C107—81no—
58C8×C107—161no—
59C22×C107—81no—
60C22×C107—81no—
61C22×C107—81no—
62C22×C107AΣL(1,𝔽16)11yescharacteristic
63C4×C107—21no—
64C4×C107—21no—
65C4×C107—21no—
66C4×C107—81no—
67C4×C107—81no—
68C4×C107—81no—
69#7521C10711yesmaximal, characteristic, direct product factor, Sylow
70C2×C107—21no—
71C2×C107—161no—
72C2×C107#140211yescharacteristic
73#1634C2×C10711yescharacteristic
74#1411C2×C10711yescharacteristic, complemented
75#1358C2×C10711yescharacteristic, complemented
76C107#752111yescharacteristic, direct product factor, Sylow
77#555C4×C10711yescharacteristic
78#494C22×C10711yescharacteristic
79#476—21no—
80#364—21no—
81#356—21no—
82#333C4×C10711yescharacteristic
83D4⋊C8—21no—
84C2×Q16—41no—
85C4⋊Q8C2×C4×C10711yescharacteristic
86C4⋊Q8D4×C10711yescharacteristic
87#124—41no—
88#121—41no—
89C4×D4—21no—
90#117—41no—
91M32—41no—
92#106—41no—
93C4⋊C8—21no—
94#102—41no—
95#101—41no—
96C4×C8D4×C10711yescharacteristic
97C2×Q8—21no—
98C2×Q8—21no—
99C2×D4—21no—
100C2×D4—41no—
101C22×C4—41no—
102Q16—81no—
103Q16—81no—
104M16—81no—
105C2×C8—21no—
106C2×C8—41no—
107C4⋊C4—21no—
108C4⋊C4—41no—
109C4⋊C4—41no—
110C22⋊C4—42no—
111C22⋊C4—41no—
112C42—41no—
113C42C22⋊C4×C10711yescharacteristic
114C16—81no—
115C23—41no—
116Q8—81no—
117Q8—81no—
118D4—41no—
119D4—41no—
120D4—161no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—81no—
126C2×C4—81no—
127C2×C4#99×C10711yescharacteristic
128C8—21no—
129C8—21no—
130C8—81no—
131C8—161no—
132C22—81no—
133C22—81no—
134C22—81no—
135C22AΣL(1,𝔽16)×C10711yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—81no—
140C4—81no—
141C4—81no—
142C2—21no—
143C2—161no—
144C2C107×#140211yescharacteristic
subgroupG/H
center, socleC2×C107#1402
commutatorC4⋊Q8C2×C4×C107
Frattini, cosocle#494C22×C107
prime radical#555×C107C4
LCSG ▷ C4⋊Q8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C22×C107 ◁ C2×C4×C107 ◁ C42×C107 ◁ #494×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#1411C2semidirect
3. C107×#1358C2semidirect
69. #7521C107direct (N × H)
74. #1411C2×C107semidirect
75. #1358C2×C107semidirect
76. C107#7521direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#16342
C107×#14112
C107×#13582
#7521107