Finite Group Databasebeta

← #31805414

Subgroups — #31805414

Order 17792.

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

normal subgroups only

This group has 210 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#22581284C212yesmaximal
3#22580883C211yesmaximal, characteristic
4#22580691C212yesmaximal
5#324×C139C211yesmaximal, characteristic
6#17984841—22no—
7#17984833—22no—
8#17984821—21no—
9#17984821C2212yes—
10#17984801—21no—
11C2×C4⋊Dic139C2211yescharacteristic
12C2×Dic139⋊C4—21no—
13#17984774—22no—
14#17984767—22no—
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—
30Dic139⋊C4—42no—
31C22⋊Dic139—22no—
32C4×Dic139—22no—
33C22×C4×C139D411yescharacteristic
34C22×C4×C139D411yescharacteristic
35C22×C4×C139C2311yescharacteristic
36C2×C8×C139—22no—
37C4⋊C4×C139—22no—
38Dic278—42no—
39Dic278—81no—
40C2×Dic139—22no—
41C2×Dic139—22no—
42C2×Dic139—22no—
43C2×Dic139—41no—
44C2×Dic139—41no—
45C2×Dic139—41no—
46C2×Dic139—41no—
47C2×Dic139—41no—
48C23×C139C2×D411yescharacteristic
49C2×C4×C139—21no—
50C2×C4×C139—21no—
51C2×C4×C139—21no—
52C2×C4×C139—41no—
53C2×C4×C139—41no—
54C2×C4×C139SD1612yes—
55C2×C4×C139C2×D412yes—
56C8×C139—42no—
57C22×C139—21no—
58C22×C139—21no—
59C22×C139#12011yescharacteristic
60C22×C139C2×SD1611yescharacteristic
61C22×C139#13711yescharacteristic
62C4×C139—22no—
63C4×C139—22no—
64C4×C139—41no—
65Dic139—42no—
66Dic139—42no—
67Dic139—42no—
68Dic139—81no—
69C2×C139—21no—
70C2×C139—21no—
71C2×C139#44811yescharacteristic
72C2×C139#45611yescharacteristic
73C2×C139#45811yescharacteristic
74C139#161111yescharacteristic, complemented, Sylow
75#1611—1391nomaximal, Sylow
76#544—1391no—
77#483—1392no—
78#398—1391no—
79#328—1392no—
80#324D13911yescharacteristic
81C4⋊Q8—2782no—
82#125—2782no—
83C22⋊Q8—2781no—
84C22⋊Q8—1392no—
85#117—2781no—
86C2×C4⋊C4—2781no—
87C2×C4⋊C4—1391no—
88C2×C4⋊C4C2×D13911yescharacteristic
89#106—2782no—
90#103—2782no—
91C22⋊C8C2×D13912yes—
92#95—2781no—
93#95—1391no—
94C2×Q8—2781no—
95C2×Q8—1392no—
96C22×C4—2781no—
97C22×C4—2781no—
98C22×C4D55611yescharacteristic
99C22×C4D55611yescharacteristic
100C22×C4C22×D13911yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—2782no—
104C4⋊C4—2781no—
105C4⋊C4—2781no—
106C4⋊C4—2781no—
107C4⋊C4—2782no—
108C4⋊C4—2782no—
109C4⋊C4—5562no—
110C4⋊C4—1392no—
111C22⋊C4—2782no—
112C42—2782no—
113C23C2×D55611yescharacteristic
114Q8—5562no—
115Q8—11121no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—2782no—
122C2×C4—2782no—
123C2×C4—2782no—
124C2×C4—5561no—
125C2×C4—5561no—
126C2×C4—5561no—
127C2×C4—5561no—
128C2×C4—5561no—
129C2×C4#1455577412yes—
130C2×C4D4×D13912yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#1798481211yescharacteristic
135C22C2×#1455577411yescharacteristic
136C22#1798487511yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—5562no—
141C4—5562no—
142C4—5562no—
143C4—11121no—
144C2—21no—
145C2—21no—
146C2#2258109411yescharacteristic
147C2#2258113811yescharacteristic
148C2#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#1611
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
74. C139#1611semidirect

Maximal subgroups

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

subgroupindex
#225815842
#225812842
#225808832
#225806912
#324×C1392
#1611139