Finite Group Databasebeta

← #31806934

Subgroups — #31806934

Order 17792.

362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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#22581520C211yesmaximal, characteristic
2#22581428C211yesmaximal, characteristic, complemented
3#22580969C212yesmaximal, complemented
4#22580710C212yesmaximal, complemented
5C2×#100×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2211yescharacteristic
7#17984838C412yescomplemented
8#17984829C412yescomplemented
9#17984813—22no—
10#17984811—22no—
11D4×Dic139—24no—
12#17984801C2211yescharacteristic
13#17984801C2212yes—
14C2×C22⋊Dic139—22no—
15#17984768—24no—
16C22×D4×C139C2211yescharacteristic
17C2×M16×C139C2212yes—
18#100×C139—22no—
19#14555785—22no—
20#14555785—22no—
21C2×Dic278C2×C411yescharacteristic, complemented
22C2×D556C2×C411yescharacteristic, complemented
23C2×C22⋊D139—24no—
24C2×C22⋊D139—21no—
25C22×Dic139—24no—
26C2×C4×D139—21no—
27C4⋊Dic139—22no—
28C4⋊Dic139—21no—
29C22⋊Dic139—24no—
30C22⋊Dic139—24no—
31C22⋊Dic139—22no—
32C22⋊Dic139—21no—
33C4×Dic139C2×C412yescomplemented
34C4×Dic139D414yescomplemented
35C24×C139D412yes—
36C2×D4×C139—22no—
37C2×D4×C139—22no—
38C2×D4×C139C2×C412yes—
39C2×D4×C139D412yes—
40C22×C4×C139C2311yescharacteristic
41M16×C139—22no—
42M16×C139—22no—
43C2×C8×C139—22no—
44C22×D139—21no—
45Dic278—22no—
46D556—22no—
47C22⋊D139—41no—
48C22⋊D139—41no—
49C22⋊D139—84no—
50C2×Dic139—22no—
51C2×Dic139—21no—
52C2×Dic139—24no—
53C2×Dic139—84no—
54C4×D139—42no—
55C23×C139—22no—
56C23×C139—22no—
57C23×C139—82no—
58C23×C139C22⋊C414yes—
59C23×C139C2×D411yescharacteristic
60D4×C139—24no—
61D4×C139—24no—
62C2×C4×C139C22×C411yescharacteristic
63C2×C4×C139C2×D412yes—
64C2×C4×C139C2×D411yescharacteristic
65C2×C4×C139#4112yes—
66C8×C139—42no—
67C22×C139—24no—
68C22×C139—41no—
69C22×C139—44no—
70C22×C139—44no—
71C22×C139—82no—
72C22×C139C2×C22⋊C411yescharacteristic
73C22×C139#12011yescharacteristic
74C22×C139#12311yescharacteristic
75C2×D139—42no—
76C2×D139—41no—
77C4×C139C4×D412yes—
78C4×C139#12112yes—
79Dic139—44no—
80Dic139—42no—
81Dic139—41no—
82C2×C139—21no—
83C2×C139—21no—
84C2×C139—21no—
85C2×C139—44no—
86C2×C139#38611yescharacteristic
87D139—81no—
88C139#191111yescharacteristic, complemented, Sylow
89#1911—1391nomaximal, Sylow
90#535—1391no—
91#518—1391no—
92#421—1392no—
93C2×#100D13911yescharacteristic, complemented
94H(3,ℤ/4)—1392no—
95C2×#41—1391no—
96C22×D4C2×D13911yescharacteristic
97C2×M16C2×D13912yes—
98#127—1392no—
99#124—1392no—
100#121—2782no—
101#120—2782no—
102C4×D4—2784no—
103#117—1392no—
104#117—1391no—
105C2×C22⋊C4—2782no—
106#104—2784no—
107#100—22no—
108C24D55612yes—
109#41—2782no—
110#41—2782no—
111C2×Q8—1391no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—2781no—
115C2×D4—2784no—
116C2×D4—1391no—
117C2×D4C4×D13912yes—
118C2×D4C22⋊D13912yes—
119C22×C4—2784no—
120C22×C4—2781no—
121C22×C4C22×D13911yescharacteristic
122M16—22no—
123M16—22no—
124C2×C8—22no—
125C4⋊C4—2782no—
126C4⋊C4—2781no—
127C22⋊C4—2784no—
128C22⋊C4—2784no—
129C22⋊C4—2782no—
130C22⋊C4—2781no—
131C42—1392no—
132C42—1394no—
133C23—22no—
134C23—22no—
135C23—82no—
136C23—2781no—
137C23(C2×D139)⋊C414yes—
138C23C2×D55611yescharacteristic
139Q8—2782no—
140D4—24no—
141D4—24no—
142D4—2782no—
143D4—5561no—
144D4—5561no—
145D4—11124no—
146C2×C4—2782no—
147C2×C4—2781no—
148C2×C4—2784no—
149C2×C4—5562no—
150C2×C4—11124no—
151C2×C4C2×C4×D13911yescharacteristic
152C2×C4D4×D13912yes—
153C2×C4C2×C22⋊D13911yescharacteristic
154C2×C4#1455578412yes—
155C8—42no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—5562no—
162C22—5561no—
163C22C2×(C2×D139)⋊C411yescharacteristic
164C22#1798481211yescharacteristic
165C22#1798482611yescharacteristic
166C4—5564no—
167C4—5562no—
168C4—5561no—
169C4(C22⋊D139)⋊C412yes—
170C4#1798481412yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—11121no—
176C2#2258083011yescharacteristic
subgroupG/H
centerC2#22580830
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
FittingC2×#100×C139C2
socleC2×C139#386
prime radical#22581520C2
cosocleC22×C4×C139C23
hypercenterC2×#100D139
hypocenterC139#1911
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #22581428C2semidirect
3. #22580969C2semidirect
4. #22580710C2semidirect
5. C2×#100×C139C2semidirect
7. #17984838C4semidirect
8. #17984829C4semidirect
21. C2×Dic278C2×C4semidirect
22. C2×D556C2×C4semidirect
33. C4×Dic139C2×C4semidirect
34. C4×Dic139D4semidirect
88. C139#1911semidirect
93. C2×#100D139semidirect

Maximal subgroups

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

subgroupindex
#225815202
#225814282
#225809692
#225807102
C2×#100×C1392
#1911139