Finite Group Databasebeta

← #31806847

Subgroups — #31806847

Order 17792.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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#22581464C211yesmaximal, characteristic
2C2×#17984770C212yesmaximal, complemented
3#22580917C211yesmaximal, characteristic, complemented
4#22580713C212yesmaximal, complemented
5C22×C42×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2211yescharacteristic
7C2×#14555769C2212yes—
8#17984825—21no—
9#17984821C412yescomplemented
10#17984816C412yescomplemented
11#17984811—21no—
12C4×C22⋊D139—22no—
13#17984801C2211yescharacteristic
14#17984770—24no—
15C22⋊(C139⋊C8)—22no—
16C23×C4×C139—21no—
17C23×C4×C139C2211yescharacteristic
18C2×C42×C139—21no—
19C2×C42×C139—24no—
20C2×C42×C139C2212yes—
21#14555785—22no—
22#14555785—22no—
23C2×Dic278C2×C411yescharacteristic, complemented
24C2×D556C2×C411yescharacteristic, complemented
25C2×C22⋊D139—22no—
26C2×C22⋊D139—21no—
27C2×C4×D139—21no—
28#14555769—22no—
29#14555769—22no—
30C2×C139⋊C8—22no—
31C4⋊Dic139C2×C412yescomplemented
32Dic139⋊C4—22no—
33C22⋊Dic139—22no—
34C22⋊Dic139—21no—
35(C2×D139)⋊C4—22no—
36C4×Dic139—21no—
37C24×C139D411yescharacteristic
38C22×C4×C139—24no—
39C22×C4×C139—28no—
40C22×C4×C139—22no—
41C22×C4×C139—22no—
42C22×C4×C139—22no—
43C22×C4×C139C2×C412yes—
44C22×C4×C139D411yescharacteristic
45C22×C4×C139D412yes—
46C22×C4×C139C2311yescharacteristic
47C42×C139—24no—
48C42×C139—22no—
49C42×C139D414yescomplemented
50C22×D139—21no—
51Dic278—22no—
52D556—22no—
53C22⋊D139—44no—
54C22⋊D139—41no—
55C22⋊D139—41no—
56C2×Dic139—22no—
57C2×Dic139—21no—
58C4×D139—42no—
59C139⋊C8—42no—
60C23×C139—24no—
61C23×C139—21no—
62C23×C139—21no—
63C23×C139C22⋊C412yes—
64C23×C139C2×D411yescharacteristic
65C2×C4×C139—216no—
66C2×C4×C139—28no—
67C2×C4×C139—21no—
68C2×C4×C139—24no—
69C2×C4×C139—21no—
70C2×C4×C139—24no—
71C2×C4×C139—24no—
72C2×C4×C139C22⋊C412yes—
73C2×C4×C139C22×C411yescharacteristic
74C2×C4×C139C2×D412yes—
75C2×C4×C139C2×D411yescharacteristic
76C2×C4×C139#4112yes—
77C22×C139—24no—
78C22×C139—24no—
79C22×C139—22no—
80C22×C139—22no—
81C22×C139—22no—
82C22×C139#10414yescomplemented
83C22×C139C2×C22⋊C411yescharacteristic
84C22×C139#12011yescharacteristic
85C22×C139#12311yescharacteristic
86C2×D139—41no—
87C2×D139—42no—
88C4×C139—28no—
89C4×C139—22no—
90C4×C139C4×D412yes—
91C4×C139#12112yes—
92Dic139—41no—
93Dic139—42no—
94C2×C139—21no—
95C2×C139—24no—
96C2×C139—21no—
97C2×C139#38611yescharacteristic
98C2×C139C2×#10412yes—
99D139—81no—
100C139#189611yescharacteristic, complemented, Sylow
101#1896—1391nomaximal, Sylow
102#525—1391no—
103C22×C42D13911yescharacteristic, complemented
104C2×#104—1392no—
105#407—1391no—
106#339—1392no—
107C2×#41—1391no—
108C23×C4—21no—
109C23×C4C2×D13911yescharacteristic
110C2×M16—1392no—
111#123—2781no—
112C22⋊Q8—1392no—
113#121—1392no—
114#120—2781no—
115C4×D4—2782no—
116#117—1391no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D13912yes—
120#104—2784no—
121C22⋊C8—2782no—
122C24C22⋊D13911yescharacteristic
123#41—2782no—
124#41—2782no—
125C2×Q8—1391no—
126C2×D4—2782no—
127C2×D4—2781no—
128C2×D4—1391no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—2781no—
135C22×C4C4×D13912yes—
136C22×C4C22⋊D13911yescharacteristic
137C22×C4D55612yes—
138C22×C4C22×D13911yescharacteristic
139M16—2782no—
140M16—2782no—
141C2×C8—2782no—
142C4⋊C4—2782no—
143C4⋊C4—1392no—
144C22⋊C4—2782no—
145C22⋊C4—2781no—
146C22⋊C4—2782no—
147C42—24no—
148C42—22no—
149C42—2781no—
150C42C22⋊D13914yescomplemented
151C23—24no—
152C23—21no—
153C23—21no—
154C23—2781no—
155C23(C2×D139)⋊C412yes—
156C23C2×C22⋊D13911yescharacteristic
157Q8—2782no—
158D4—2782no—
159D4—5564no—
160D4—5561no—
161D4—5561no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—2782no—
170C2×C4—2781no—
171C2×C4—5562no—
172C2×C4(C2×D139)⋊C412yes—
173C2×C4C2×C4×D13911yescharacteristic
174C2×C4C2×C22⋊D13912yes—
175C2×C4C2×D55611yescharacteristic
176C2×C4#1455578512yes—
177C8—5562no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—5561no—
184C22—5562no—
185C22#1798477014yescomplemented
186C22C2×(C2×D139)⋊C411yescharacteristic
187C22#1798481111yescharacteristic
188C22#1798482511yescharacteristic
189C4—28no—
190C4—22no—
191C4—5561no—
192C4—5562no—
193C4C4×C22⋊D13912yes—
194C4#1798481612yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—11121no—
199C2#2258083211yescharacteristic
200C2C2×#1798477012yes—
subgroupG/H
centerC2×C4C2×D556
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
FittingC22×C42×C139C2
socleC22×C139C2×C22⋊C4
prime radical#22581464C2
cosocleC22×C4×C139C23
hypercenterC22×C42D139
hypocenterC139#1896
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#17984770C2semidirect
3. #22580917C2semidirect
4. #22580713C2semidirect
5. C22×C42×C139C2semidirect
9. #17984821C4semidirect
10. #17984816C4semidirect
23. C2×Dic278C2×C4semidirect
24. C2×D556C2×C4semidirect
31. C4⋊Dic139C2×C4semidirect
49. C42×C139D4semidirect
82. C22×C139#104semidirect
100. C139#1896semidirect
103. C22×C42D139semidirect
150. C42C22⋊D139semidirect
185. C22#17984770semidirect

Maximal subgroups

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

subgroupindex
#225814642
C2×#179847702
#225809172
#225807132
C22×C42×C1392
#1896139