Finite Group Databasebeta

← #31805700

Subgroups — #31805700

Order 17792.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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
1#22581703C211yesmaximal, characteristic, complemented
2#22581317C212yesmaximal, complemented
3#22580694C212yesmaximal, complemented
4#22580693C211yesmaximal, characteristic, complemented
5#496×C139C211yesmaximal, characteristic
6#17984840—21no—
7#17984835—22no—
8#17984834C2212yes—
9#17984823—21no—
10#17984819—22no—
11#17984763—22no—
12#17984763—22no—
13#17984753C2212yes—
14C2×SD16×C139—21no—
15C2×D8×C139—21no—
16#127×C139C2211yescharacteristic
17#124×C139C2211yescharacteristic
18#97×C139C2211yescharacteristic
19C2×Dic278—21no—
20C22×Dic139—21no—
21C2×C139⋊C8—22no—
22C4⋊Dic139D412yes—
23C4⋊Dic139D412yes—
24Dic139⋊C4—22no—
25Dic139⋊C4—22no—
26Dic139⋊C4—22no—
27C22⋊Dic139—22no—
28C22⋊Dic139—21no—
29C4×Dic139—21no—
30C2×Q8×C139D411yescharacteristic
31C2×D4×C139—21no—
32C2×D4×C139—22no—
33C2×D4×C139D411yescharacteristic
34SD16×C139—42no—
35D8×C139—42no—
36C2×C8×C139—21no—
37C22⋊C4×C139—22no—
38C42×C139C2311yescharacteristic
39Dic278—81no—
40C2×Dic139—22no—
41C2×Dic139—22no—
42C2×Dic139—81no—
43C139⋊C8—42no—
44C23×C139—21no—
45C23×C139—41no—
46Q8×C139—41no—
47D4×C139—41no—
48D4×C139—41no—
49D4×C139—41no—
50D4×C139—44no—
51C2×C4×C139—21no—
52C2×C4×C139C2×D412yes—
53C2×C4×C139C2×D411yescharacteristic
54C8×C139—22no—
55C22×C139—41no—
56C22×C139—42no—
57C22×C139—81no—
58C22×C139—82no—
59C22×C139#12011yescharacteristic
60C4×C139—21no—
61C4×C139—22no—
62C4×C139—41no—
63Dic139—42no—
64Dic139—42no—
65C2×C139—81no—
66C2×C139—161no—
67C2×C139#45311yescharacteristic
68C2×C139#45412yes—
69C139#165711yescharacteristic, complemented, Sylow
70#1657—1391nomaximal, Sylow
71#563—1391no—
72#496D13911yescharacteristic
73#490—1392no—
74#330—1392no—
75#329—1391no—
76C2×SD16—21no—
77C2×D8—21no—
78C4⋊Q8—2781no—
79#127C2×D13911yescharacteristic
80#126—2782no—
81#125—1392no—
82#124C2×D13911yescharacteristic
83#123—2781no—
84C22⋊Q8—2782no—
85#102—2782no—
86#102—2782no—
87#97—1392no—
88#97C2×D13911yescharacteristic
89C2×Q8—2781no—
90C2×Q8C22⋊D13911yescharacteristic
91C2×D4—22no—
92C2×D4—21no—
93C2×D4C22⋊D13911yescharacteristic
94C22×C4—2781no—
95SD16—42no—
96D8—42no—
97C2×C8—21no—
98C2×C8—2782no—
99C4⋊C4—2782no—
100C4⋊C4—2782no—
101C4⋊C4—2782no—
102C4⋊C4—1392no—
103C4⋊C4—1392no—
104C22⋊C4—22no—
105C22⋊C4—2782no—
106C22⋊C4—2781no—
107C42—2781no—
108C42C22×D13911yescharacteristic
109C23—21no—
110C23—41no—
111Q8—41no—
112Q8—11121no—
113D4—41no—
114D4—41no—
115D4—41no—
116D4—44no—
117C2×C4—21no—
118C2×C4—2782no—
119C2×C4—2782no—
120C2×C4—11121no—
121C2×C4D4×D13912yes—
122C2×C4C2×C22⋊D13911yescharacteristic
123C8—22no—
124C8—5562no—
125C22—41no—
126C22—42no—
127C22—81no—
128C22—82no—
129C22#1798481011yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—5562no—
134C4—5562no—
135C2—81no—
136C2—161no—
137C2#2258112011yescharacteristic
138C2#2258112412yes—
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting, prime radical#496×C139C2
socleC22×C139#120
hypercenter#496D139
hypocenterC139#1657
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #22581703C2semidirect
2. #22581317C2semidirect
3. #22580694C2semidirect
4. #22580693C2semidirect
69. C139#1657semidirect

Maximal subgroups

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

subgroupindex
#225817032
#225813172
#225806942
#225806932
#496×C1392
#1657139