Finite Group Databasebeta

← #31816656

Subgroups — #31816656

Order 17792.

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

normal subgroups only

This group has 394 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#22581565C211yesmaximal, characteristic, complemented
2#22581294C212yesmaximal, complemented
3#22581253C212yesmaximal, complemented
4#22581158C212yesmaximal, complemented
5#22581104C212yesmaximal
6#22581053C212yesmaximal, complemented
7C4×#14555773C212yesmaximal, complemented
8#22581014C211yesmaximal, characteristic, complemented
9#518×C139C211yesmaximal, characteristic
10C2×#14555773C2212yes—
11C2×#14555773C2212yes—
12#17984842C2211yescharacteristic, complemented
13#17984835—22no—
14#17984834C2211yescharacteristic, complemented
15#17984832—22no—
16#17984821C2212yes—
17C4×Dic278C2212yescomplemented
18#17984775C2212yescomplemented
19#17984773C2212yescomplemented
20C4⋊(C139⋊C8)C2212yescomplemented
21#17984765C2212yescomplemented
22#17984765C2212yescomplemented
23#17984763C2212yes—
24#17984763C2212yes—
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×Dic278C2312yes—
36#14555773—24no—
37#14555773—24no—
38C2×C139⋊C8C2312yes—
39C2×C139⋊C8C2312yes—
40C4⋊Dic139—22no—
41C4⋊Dic139C2312yes—
42Dic139⋊C4—22no—
43Dic139⋊C4—22no—
44Dic139⋊C4—22no—
45C22⋊Dic139—22no—
46C4×Dic139—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
63Dic278—22no—
64Dic278—22no—
65C2×Dic139—22no—
66C2×Dic139—22no—
67C139⋊C8—22no—
68C139⋊C8—22no—
69C23×C139—24no—
70C23×C139—22no—
71C23×C139—82no—
72C23×C139C2×D411yescharacteristic
73D4×C139—24no—
74D4×C139—22no—
75D4×C139#4114yes—
76C2×C4×C139—22no—
77C2×C4×C139—22no—
78C2×C4×C139—82no—
79C2×C4×C139—82no—
80C2×C4×C139C2×D411yescharacteristic
81C2×C4×C139C2×D412yes—
82C2×C4×C139C2×D412yes—
83C2×C4×C139C2411yescharacteristic
84C22×C139—21no—
85C22×C139—24no—
86C22×C139—22no—
87C22×C139—42no—
88C22×C139—42no—
89C22×C139—84no—
90C22×C139C22×D411yescharacteristic
91C4×C139—21no—
92C4×C139—22no—
93C4×C139—22no—
94C4×C139—42no—
95C4×C139C2×#4112yes—
96Dic139—42no—
97Dic139—42no—
98C2×C139—41no—
99C2×C139—44no—
100C2×C139#52511yescharacteristic
101C2×C139#57712yes—
102C139#312311yescharacteristic, complemented, Sylow
103#3123—1391nomaximal, Sylow
104#541—1391no—
105#518D13911yescharacteristic
106#485—1392no—
107#478—1392no—
108#461—1392no—
109#450—1392no—
110#440—1392no—
111C4×SD16—1392no—
112#433—1391no—
113C22×D4C2×D13911yescharacteristic
114C2×SD16—1392no—
115C2×SD16—1392no—
116C4⋊Q8—1391no—
117#126—2782no—
118#125—2782no—
119#125—1391no—
120C22⋊Q8—1392no—
121C4×Q8—1392no—
122C4×D4—22no—
123C4×D4C2×D13912yes—
124C4×D4C2×D13912yes—
125#117C2×D13911yescharacteristic
126#117C2×D13911yescharacteristic
127C2×C22⋊C4—22no—
128#107—1392no—
129#106—1392no—
130C4⋊C8—1392no—
131#103—1392no—
132#103—1392no—
133#102—1392no—
134#102—1392no—
135C22⋊C8—1392no—
136#97—1391no—
137C4×C8—1391no—
138C24—21no—
139C2×Q8—1392no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D13912yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D13911yescharacteristic
146SD16—2784no—
147SD16—2784no—
148C2×C8—1392no—
149C2×C8—1392no—
150C4⋊C4—2782no—
151C4⋊C4—2782no—
152C4⋊C4—2782no—
153C4⋊C4—2782no—
154C4⋊C4—1392no—
155C4⋊C4C22⋊D13912yes—
156C4⋊C4C22×D13912yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—2782no—
161C22⋊C4C22⋊D13912yes—
162C42—21no—
163C42—2782no—
164C42C22×D13911yescharacteristic
165C42C22×D13911yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D13911yescharacteristic
170Q8—2782no—
171Q8—2782no—
172D4—24no—
173D4—22no—
174D4#1455578514yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—2782no—
180C2×C4—2782no—
181C2×C4C2×C22⋊D13911yescharacteristic
182C2×C4C2×C22⋊D13912yes—
183C2×C4C2×C22⋊D13912yes—
184C2×C4C23×D13911yescharacteristic
185C8—2782no—
186C8—2782no—
187C22—22no—
188C22—21no—
189C22—24no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D13911yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—42no—
198C4—5562no—
199C4—5562no—
200C4C2×#1455578512yes—
201C2—41no—
202C2—44no—
203C2#2258146411yescharacteristic
204C2#2258176412yes—
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#518×C139C2
socleC22×C139C22×D4
prime radicalC22×D4×C139C22
hypercenter#518D139
hypocenterC139#3123
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. #22581565C2semidirect
2. #22581294C2semidirect
3. #22581253C2semidirect
4. #22581158C2semidirect
6. #22581053C2semidirect
7. C4×#14555773C2semidirect
8. #22581014C2semidirect
12. #17984842C22semidirect
14. #17984834C22semidirect
17. C4×Dic278C22semidirect
18. #17984775C22semidirect
19. #17984773C22semidirect
20. C4⋊(C139⋊C8)C22semidirect
21. #17984765C22semidirect
22. #17984765C22semidirect
26. #17984753C22semidirect
27. C4×C139⋊C8C22semidirect
102. C139#3123semidirect

Maximal subgroups

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

subgroupindex
#225815652
#225812942
#225812532
#225811582
#225811042
#225810532
C4×#145557732
#225810142
#518×C1392
#3123139