Finite Group Databasebeta

← #31805448

Subgroups — #31805448

Order 17792.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#22581584C211yesmaximal, characteristic
2#22581289C212yesmaximal
3#22580892C211yesmaximal, characteristic
4#22580691C212yesmaximal
5#324×C139C211yesmaximal, characteristic
6#17984841—22no—
7#17984833—22no—
8#17984821—21no—
9#17984821C2212yes—
10#17984801—21no—
11C2×C4⋊Dic139C2211yescharacteristic
12#17984776—22no—
13#17984767—22no—
14C139⋊#95—21no—
15C139⋊#95—21no—
16C139⋊#95C2211yescharacteristic
17C2×C4⋊C4×C139C2211yescharacteristic
18C22⋊C8×C139C2212yes—
19C2×Dic278—21no—
20C2×Dic278D412yes—
21C22×Dic139—21no—
22C22×Dic139—21no—
23C4⋊Dic139—21no—
24C4⋊Dic139—21no—
25C4⋊Dic139—21no—
26C4⋊Dic139—22no—
27C4⋊Dic139D412yes—
28Dic139⋊C4—22no—
29Dic139⋊C4—22no—
30C22⋊Dic139—22no—
31C4×Dic139—22no—
32C22×C4×C139D411yescharacteristic
33C22×C4×C139D411yescharacteristic
34C22×C4×C139C2311yescharacteristic
35C2×C8×C139—22no—
36C4⋊C4×C139—22no—
37Dic278—42no—
38Dic278—81no—
39C2×Dic139—22no—
40C2×Dic139—22no—
41C2×Dic139—41no—
42C2×Dic139—41no—
43C2×Dic139—42no—
44C2×Dic139—41no—
45C2×Dic139—41no—
46C23×C139C2×D411yescharacteristic
47C2×C4×C139—21no—
48C2×C4×C139—21no—
49C2×C4×C139—21no—
50C2×C4×C139—41no—
51C2×C4×C139—41no—
52C2×C4×C139Q1612yes—
53C2×C4×C139C2×D412yes—
54C8×C139—42no—
55C22×C139—21no—
56C22×C139—21no—
57C22×C139#12011yescharacteristic
58C22×C139C2×Q1611yescharacteristic
59C22×C139#13711yescharacteristic
60C4×C139—22no—
61C4×C139—22no—
62C4×C139—41no—
63Dic139—42no—
64Dic139—42no—
65Dic139—81no—
66Dic139—81no—
67C2×C139—21no—
68C2×C139—21no—
69C2×C139#45111yescharacteristic
70C2×C139#45411yescharacteristic
71C2×C139#45811yescharacteristic
72C139#161711yescharacteristic, complemented, Sylow
73#1617—1391nomaximal, Sylow
74#544—1391no—
75#484—1392no—
76#400—1391no—
77#328—1392no—
78#324D13911yescharacteristic
79C4⋊Q8—2782no—
80#125—2782no—
81C22⋊Q8—2781no—
82C22⋊Q8—1392no—
83#117—2781no—
84C2×C4⋊C4—1391no—
85C2×C4⋊C4C2×D13911yescharacteristic
86#107—2782no—
87#103—2782no—
88C22⋊C8C2×D13912yes—
89#95—2781no—
90#95—2781no—
91#95—1391no—
92C2×Q8—2781no—
93C2×Q8—1392no—
94C22×C4—2781no—
95C22×C4—2781no—
96C22×C4D55611yescharacteristic
97C22×C4D55611yescharacteristic
98C22×C4C22×D13911yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—2782no—
102C4⋊C4—2781no—
103C4⋊C4—2781no—
104C4⋊C4—2781no—
105C4⋊C4—2782no—
106C4⋊C4—2782no—
107C4⋊C4—1392no—
108C22⋊C4—2782no—
109C42—2782no—
110C23C2×D55611yescharacteristic
111Q8—5562no—
112Q8—11121no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—2782no—
119C2×C4—2782no—
120C2×C4—5561no—
121C2×C4—5561no—
122C2×C4—5562no—
123C2×C4—5561no—
124C2×C4—5561no—
125C2×C4Dic55612yes—
126C2×C4D4×D13912yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1798481211yescharacteristic
131C22C2×Dic55611yescharacteristic
132C22#1798487511yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—5562no—
137C4—5562no—
138C4—11121no—
139C4—11121no—
140C2—21no—
141C2—21no—
142C2#2258111111yescharacteristic
143C2#2258112811yescharacteristic
144C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#324×C139C2
socleC22×C139#120
prime radicalC23×C139C2×D4
hypercenter#324D139
hypocenterC139#1617
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
72. C139#1617semidirect

Maximal subgroups

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

subgroupindex
#225815842
#225812892
#225808922
#225806912
#324×C1392
#1617139