Finite Group Databasebeta

← #31816647

Subgroups — #31816647

Order 17792.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#22581558C211yesmaximal, characteristic, complemented
2#22581277C212yesmaximal, complemented
3#22581253C212yesmaximal, complemented
4#22581148C212yesmaximal, complemented
5#22581087C212yesmaximal, complemented
6#22581063C212yesmaximal, complemented
7C4×#14555770C212yesmaximal, complemented
8#22581014C211yesmaximal, characteristic, complemented
9#518×C139C211yesmaximal, characteristic, complemented
10C2×#14555770C2212yes—
11C2×#14555770C2212yes—
12#17984839C2211yescharacteristic, complemented
13#17984834C2211yescharacteristic, complemented
14#17984827—22no—
15#17984816C2212yes—
16#17984815—22no—
17C4×D556C2212yescomplemented
18#17984775C2212yescomplemented
19#17984773C2212yescomplemented
20C4⋊(C139⋊C8)C2212yescomplemented
21#17984763C2212yes—
22#17984763C2212yes—
23#17984762C2212yescomplemented
24#17984762C2212yescomplemented
25C22⋊(C139⋊C8)C2212yes—
26#17984753C2211yescharacteristic, complemented
27C4×C139⋊C8C2211yescharacteristic, complemented
28C22×D4×C139C2211yescharacteristic
29C4×D4×C139—22no—
30C4×D4×C139C2212yes—
31C4×D4×C139C2212yes—
32#117×C139C2211yescharacteristic
33#117×C139C2211yescharacteristic
34C2×C22⋊C4×C139—22no—
35C2×D556—22no—
36C2×D556C2312yes—
37C2×C22⋊D139—22no—
38C2×C4×D139—22no—
39#14555770—24no—
40#14555770—24no—
41C2×C139⋊C8C2312yes—
42C2×C139⋊C8C2312yes—
43C4⋊Dic139C2312yes—
44Dic139⋊C4—22no—
45(C2×D139)⋊C4—22no—
46(C2×D139)⋊C4—22no—
47C24×C139—21no—
48C2×D4×C139—24no—
49C2×D4×C139—21no—
50C2×D4×C139C2312yes—
51C22×C4×C139—22no—
52C22×C4×C139—22no—
53C22×C4×C139C2311yescharacteristic
54C4⋊C4×C139D412yes—
55C4⋊C4×C139C2312yes—
56C22⋊C4×C139—21no—
57C22⋊C4×C139—22no—
58C22⋊C4×C139—22no—
59C22⋊C4×C139D412yes—
60C42×C139—21no—
61C42×C139C2311yescharacteristic
62C42×C139C2311yescharacteristic
63C22×D139—22no—
64D556—22no—
65D556—22no—
66D556—82no—
67C22⋊D139—82no—
68C2×Dic139—22no—
69C4×D139—82no—
70C139⋊C8—22no—
71C139⋊C8—22no—
72C23×C139—24no—
73C23×C139—22no—
74C23×C139—82no—
75C23×C139C2×D411yescharacteristic
76D4×C139—24no—
77D4×C139—22no—
78D4×C139#4114yes—
79C2×C4×C139—22no—
80C2×C4×C139—22no—
81C2×C4×C139—82no—
82C2×C4×C139—82no—
83C2×C4×C139C2×D411yescharacteristic
84C2×C4×C139C2×D412yes—
85C2×C4×C139C2×D412yes—
86C2×C4×C139C2411yescharacteristic
87C22×C139—21no—
88C22×C139—24no—
89C22×C139—22no—
90C22×C139—42no—
91C22×C139—42no—
92C22×C139—84no—
93C22×C139C22×D411yescharacteristic
94C2×D139—42no—
95C2×D139—42no—
96C2×D139—42no—
97C4×C139—21no—
98C4×C139—22no—
99C4×C139—22no—
100C4×C139—42no—
101C4×C139C2×#4112yes—
102Dic139—42no—
103C2×C139—41no—
104C2×C139—44no—
105C2×C139#52511yescharacteristic
106C2×C139#57612yes—
107D139—82no—
108C139#312211yescharacteristic, complemented, Sylow
109#3122—1391nomaximal, Sylow
110#540—1391no—
111#518D13911yescharacteristic, complemented
112#482—1392no—
113#478—1392no—
114#459—1392no—
115#447—1392no—
116#442—1392no—
117C4×D8—1392no—
118#433—1391no—
119C22×D4C2×D13911yescharacteristic
120C2×D8—1392no—
121C2×D8—1392no—
122#127—1391no—
123#125—1391no—
124#123—2782no—
125#121—2782no—
126#121—1392no—
127C4×D4—22no—
128C4×D4—1392no—
129C4×D4C2×D13912yes—
130C4×D4C2×D13912yes—
131#117C2×D13911yescharacteristic
132#117C2×D13911yescharacteristic
133C2×C22⋊C4—22no—
134#107—1392no—
135#106—1392no—
136C4⋊C8—1392no—
137#102—1392no—
138#102—1392no—
139#102—1392no—
140#102—1392no—
141C22⋊C8—1392no—
142#97—1391no—
143C4×C8—1391no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—2782no—
148C2×D4—2782no—
149C2×D4—1392no—
150C2×D4C22×D13912yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—2782no—
154C22×C4C22×D13911yescharacteristic
155D8—2784no—
156D8—2784no—
157C2×C8—1392no—
158C2×C8—1392no—
159C4⋊C4—2782no—
160C4⋊C4—1392no—
161C4⋊C4C22⋊D13912yes—
162C4⋊C4C22×D13912yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—2782no—
167C22⋊C4—2782no—
168C22⋊C4C22⋊D13912yes—
169C42—21no—
170C42C22×D13911yescharacteristic
171C42C22×D13911yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—2782no—
176C23C2×C22⋊D13911yescharacteristic
177D4—24no—
178D4—22no—
179D4—2782no—
180D4—2782no—
181D4—11122no—
182D4—11122no—
183D4#1455578514yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—2782no—
189C2×C4—11122no—
190C2×C4C2×C22⋊D13911yescharacteristic
191C2×C4C2×C22⋊D13912yes—
192C2×C4C2×C22⋊D13912yes—
193C2×C4C23×D13911yescharacteristic
194C8—2782no—
195C8—2782no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—5562no—
203C22—5562no—
204C22—5562no—
205C22C22×C22⋊D13911yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—5562no—
211C4C2×#1455578512yes—
212C2—41no—
213C2—44no—
214C2—11122no—
215C2#2258146411yescharacteristic
216C2#2258175612yes—
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#518×C139C2
socleC22×C139C22×D4
hypercenter#518D139
hypocenterC139#3122
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #22581558C2semidirect
2. #22581277C2semidirect
3. #22581253C2semidirect
4. #22581148C2semidirect
5. #22581087C2semidirect
6. #22581063C2semidirect
7. C4×#14555770C2semidirect
8. #22581014C2semidirect
9. #518×C139C2semidirect
12. #17984839C22semidirect
13. #17984834C22semidirect
17. C4×D556C22semidirect
18. #17984775C22semidirect
19. #17984773C22semidirect
20. C4⋊(C139⋊C8)C22semidirect
23. #17984762C22semidirect
24. #17984762C22semidirect
26. #17984753C22semidirect
27. C4×C139⋊C8C22semidirect
108. C139#3122semidirect
111. #518D139semidirect

Maximal subgroups

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

subgroupindex
#225815582
#225812772
#225812532
#225811482
#225810872
#225810632
C4×#145557702
#225810142
#518×C1392
#3122139