Finite Group Databasebeta

← #31805026

Subgroups — #31805026

Order 17792.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D139C211yesmaximal, characteristic
2#22581008C212yesmaximal, complemented
3#22580693C211yesmaximal, characteristic, complemented
4#22580692C212yesmaximal, complemented
5#329×C139C211yesmaximal, characteristic, complemented
6C2×Q8×D139C411yescharacteristic
7C2×D4×D139C411yescharacteristic
8#17984831C411yescharacteristic
9#17984830C2211yescharacteristic
10#17984829C411yescharacteristic
11#17984828—22no—
12C22⋊C4×D139—22no—
13C42×D139C2211yescharacteristic
14Dic139⋊C8—22no—
15(C2×D139)⋊C8—22no—
16#17984753C2212yescomplemented
17#124×C139C2211yescharacteristic
18#97×C139C2212yescomplemented
19C23×D139—21no—
20C2×Dic278—21no—
21C2×Dic278C2×C411yescharacteristic
22Q8×D139—42no—
23C2×D556C2×C411yescharacteristic
24C2×C22⋊D139—21no—
25D4×D139—42no—
26C2×C4×D139—21no—
27C2×C4×D139C2×C411yescharacteristic
28C2×C4×D139D412yes—
29C2×C139⋊C8—22no—
30C22⋊Dic139—22no—
31(C2×D139)⋊C4—22no—
32(C2×D139)⋊C4—22no—
33C4×Dic139C2×C411yescharacteristic
34C4×Dic139D412yes—
35C2×Q8×C139C2×C411yescharacteristic
36C2×D4×C139C2×C411yescharacteristic
37C2×C8×C139—22no—
38C22⋊C4×C139—22no—
39C42×C139C2311yescharacteristic
40C22×D139—21no—
41C22×D139—44no—
42C22×D139—42no—
43C22×D139C22⋊C411yescharacteristic
44Dic278—42no—
45Dic278—41no—
46D556—41no—
47C22⋊D139—42no—
48C2×Dic139—21no—
49C2×Dic139C22⋊C412yes—
50C2×Dic139C22⋊C411yescharacteristic
51C4×D139—22no—
52C4×D139—42no—
53C4×D139—42no—
54C139⋊C8—42no—
55C23×C139—21no—
56Q8×C139—41no—
57D4×C139—41no—
58C2×C4×C139—21no—
59C2×C4×C139C22×C411yescharacteristic
60C2×C4×C139C2×D412yes—
61C8×C139—42no—
62C22×C139—41no—
63C22×C139—42no—
64C22×C139C2×C22⋊C411yescharacteristic
65C2×D139—22no—
66C2×D139—41no—
67C2×D139—42no—
68C2×D139—84no—
69C2×D139#10012yes—
70C4×C139—21no—
71C4×C139—22no—
72C4×C139—41no—
73Dic139—21no—
74Dic139—22no—
75Dic139—41no—
76C2×C139—81no—
77C2×C139C2×#10011yescharacteristic
78C2×C139#42112yes—
79D139—22no—
80D139—81no—
81C139#153311yescharacteristic, complemented, Sylow
82#1533—1391nomaximal, Sylow
83C2×#124—1391no—
84#432—1392no—
85#329—1391no—
86#329—1392no—
87#329D13911yescharacteristic, complemented
88C22×Q8—1391no—
89C22×D4—1391no—
90#124—2782no—
91#124—1391no—
92#124—1391no—
93#124—1391no—
94#124C2×D13911yescharacteristic
95C2×C22⋊C4—2782no—
96C2×C42—1391no—
97C4⋊C8—2782no—
98C22⋊C8—2782no—
99#97—1392no—
100#97C2×D13912yescomplemented
101C24—2781no—
102C2×Q8—2781no—
103C2×Q8—5562no—
104C2×Q8—1391no—
105C2×Q8C4×D13911yescharacteristic
106C2×D4—2781no—
107C2×D4—5562no—
108C2×D4—1391no—
109C2×D4C4×D13911yescharacteristic
110C22×C4—2781no—
111C22×C4—1391no—
112C22×C4—1392no—
113C2×C8—22no—
114C2×C8—2782no—
115C22⋊C4—22no—
116C22⋊C4—2782no—
117C22⋊C4—2782no—
118C22⋊C4—2782no—
119C42—1391no—
120C42—1392no—
121C42C22×D13911yescharacteristic
122C23—21no—
123C23—2781no—
124C23—5564no—
125C23—5562no—
126C23—1391no—
127Q8—41no—
128Q8—5561no—
129Q8—5562no—
130D4—41no—
131D4—5561no—
132D4—5562no—
133C2×C4—21no—
134C2×C4—2782no—
135C2×C4—2781no—
136C2×C4—5562no—
137C2×C4—5562no—
138C2×C4—1392no—
139C2×C4—1391no—
140C2×C4C2×C4×D13911yescharacteristic
141C2×C4D4×D13912yes—
142C8—42no—
143C8—5562no—
144C22—41no—
145C22—42no—
146C22—2782no—
147C22—5561no—
148C22—5562no—
149C22—11124no—
150C22—1392no—
151C22C22⋊C4×D13911yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—2781no—
156C4—2782no—
157C4—5561no—
158C2—81no—
159C2—2782no—
160C2—11121no—
161C2#100×D13911yescharacteristic
162C2#2258096812yes—
subgroupG/H
centerC22C22⋊C4×D139
commutatorC2×C4×C139C22×C4
FrattiniC42C22×D139
Fitting#329×C139C2
socleC22×C139C2×C22⋊C4
prime radicalC2×D4×D139C4
cosocleC42×C139C23
hypercenter#329D139
hypocenterC139#1533
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #22581008C2semidirect
3. #22580693C2semidirect
4. #22580692C2semidirect
5. #329×C139C2semidirect
16. #17984753C22semidirect
18. #97×C139C22semidirect
81. C139#1533semidirect
87. #329D139semidirect
100. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
#124×D1392
#225810082
#225806932
#225806922
#329×C1392
#1533139