Finite Group Databasebeta

← #31816868

Subgroups — #31816868

Order 17792.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#17984873C212yesmaximal, complemented
2C2×#17984868C212yesmaximal, complemented
3#22581503C211yesmaximal, characteristic, complemented
4#22581348C212yesmaximal, complemented
5#22581343C212yesmaximal, complemented
6#22581335C214yesmaximal, complemented
7C4×#14555769C211yesmaximal, characteristic, complemented
8C2×#124×C139C211yesmaximal, characteristic, complemented
9C2×#14555785C2212yes—
10#17984873—28no—
11#17984868—28no—
12C2×#14555775C2214yescomplemented
13C2×#14555773C2214yes—
14C2×#14555772C2214yescomplemented
15C2×#14555770C2214yes—
16C2×#14555769C2212yes—
17#17984842C2211yescharacteristic, complemented
18#17984839C2211yescharacteristic, complemented
19#17984830C2212yescomplemented
20#17984816—22no—
21C4×D556—22no—
22#17984753C2212yescomplemented
23C4×C139⋊C8C2212yescomplemented
24C22×Q8×C139C2211yescharacteristic
25C22×D4×C139C2211yescharacteristic
26#124×C139—22no—
27#124×C139C2212yes—
28#124×C139C2212yes—
29C2×C22⋊C4×C139—22no—
30C2×C42×C139C2211yescharacteristic
31#14555785—24no—
32#14555785—24no—
33C2×Dic278C2312yes—
34C2×D556—22no—
35C2×D556C2312yes—
36C2×C22⋊D139—22no—
37C2×C4×D139—22no—
38#14555775—28no—
39#14555773—28no—
40#14555772—28no—
41#14555770—28no—
42#14555769D418yescomplemented
43C2×C139⋊C8C2314yes—
44C4⋊Dic139—22no—
45(C2×D139)⋊C4—24no—
46C24×C139—21no—
47C2×Q8×C139—21no—
48C2×Q8×C139—24no—
49C2×Q8×C139C2312yes—
50C2×D4×C139—24no—
51C2×D4×C139—21no—
52C2×D4×C139C2312yes—
53C22×C4×C139—21no—
54C22×C4×C139D412yes—
55C22×C4×C139C2311yescharacteristic
56C22⋊C4×C139—24no—
57C22⋊C4×C139—24no—
58C42×C139D412yes—
59C42×C139C2311yescharacteristic
60C42×C139C2311yescharacteristic
61C22×D139—22no—
62Dic278—22no—
63Dic278—22no—
64D556—22no—
65D556—22no—
66D556—44no—
67C22⋊D139—44no—
68C2×Dic139—22no—
69C4×D139—44no—
70C139⋊C8C2×D418yes—
71C23×C139—22no—
72C23×C139—44no—
73C23×C139—42no—
74C23×C139C2×D411yescharacteristic
75Q8×C139—24no—
76Q8×C139—42no—
77D4×C139—24no—
78D4×C139—42no—
79C2×C4×C139—22no—
80C2×C4×C139—42no—
81C2×C4×C139—42no—
82C2×C4×C139C2×D414yes—
83C2×C4×C139C2×D412yes—
84C2×C4×C139C2×D412yes—
85C2×C4×C139C2×D411yescharacteristic
86C2×C4×C139C2411yescharacteristic
87C22×C139—22no—
88C22×C139—42no—
89C22×C139—44no—
90C22×C139—84no—
91C22×C139#12712yes—
92C22×C139C22×D411yescharacteristic
93C2×D139—42no—
94C2×D139—44no—
95C4×C139—22no—
96C4×C139—22no—
97C4×C139—42no—
98C4×C139#12712yes—
99C4×C139C22×D412yes—
100Dic139—42no—
101C2×C139—22no—
102C2×C139—82no—
103C2×C139C2×#12711yescharacteristic
104C2×C139#57512yes—
105D139—82no—
106C139#315311yescharacteristic, complemented, Sylow
107#3153—1391nomaximal, Sylow
108C2×#137—1392no—
109C2×AGL(1,ℤ/8)—1392no—
110#532—1391no—
111C2×#124D13911yescharacteristic, complemented
112#497—1392no—
113#496—1392no—
114#495—1394no—
115C4×M16—1391no—
116C2×#41—1392no—
117C22×Q8C2×D13911yescharacteristic
118C22×D4C2×D13911yescharacteristic
119#137—2788no—
120AGL(1,ℤ/8)—2788no—
121C2×Q16—1394no—
122C2×SD16—1394no—
123C2×SD16—1394no—
124C2×D8—1394no—
125C2×M16—1392no—
126C4⋊Q8—1391no—
127#127—1391no—
128#124—22no—
129#124—1392no—
130#124C2×D13912yes—
131#124C2×D13912yes—
132#121—2782no—
133C4×D4—2782no—
134C2×C22⋊C4—22no—
135C2×C42C2×D13911yescharacteristic
136#97—1392no—
137C4×C8—1392no—
138C24—21no—
139#41—2784no—
140#41—2784no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—1392no—
144C2×Q8C22×D13912yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—2782no—
148C2×D4—2782no—
149C2×D4—1392no—
150C2×D4C22×D13912yes—
151C22×C4—21no—
152C22×C4—2782no—
153C22×C4C22⋊D13912yes—
154C22×C4C22×D13911yescharacteristic
155Q16—2788no—
156SD16—2788no—
157SD16—2788no—
158D8—2788no—
159M16—1398no—
160C2×C8—1394no—
161C4⋊C4—2782no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—2784no—
165C42C22⋊D13912yes—
166C42C22×D13911yescharacteristic
167C42C22×D13911yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—2782no—
172C23C2×C22⋊D13911yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—2782no—
176Q8—2782no—
177D4—24no—
178D4—42no—
179D4—2782no—
180D4—2782no—
181D4—5564no—
182D4—5564no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—2782no—
187C2×C4—5564no—
188C2×C4D4×D13914yes—
189C2×C4C2×C22⋊D13912yes—
190C2×C4C2×C22⋊D13912yes—
191C2×C4C2×C22⋊D13911yescharacteristic
192C2×C4C23×D13911yescharacteristic
193C8—1398no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—5562no—
199C22—5564no—
200C22#1798483812yes—
201C22C22×C22⋊D13911yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—5562no—
206C4#1798483812yes—
207C4C2×D4×D13912yes—
208C2—22no—
209C2—82no—
210C2—11122no—
211C2C2×#1798483811yescharacteristic
212C2#2258175112yes—
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×#124×C139C2
socleC22×C139C22×D4
hypercenterC2×#124D139
hypocenterC139#3153
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#17984873C2semidirect
2. C2×#17984868C2semidirect
3. #22581503C2semidirect
4. #22581348C2semidirect
5. #22581343C2semidirect
6. #22581335C2semidirect
7. C4×#14555769C2semidirect
8. C2×#124×C139C2semidirect
12. C2×#14555775C22semidirect
14. C2×#14555772C22semidirect
17. #17984842C22semidirect
18. #17984839C22semidirect
19. #17984830C22semidirect
22. #17984753C22semidirect
23. C4×C139⋊C8C22semidirect
42. #14555769D4semidirect
106. C139#3153semidirect
111. C2×#124D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848732
C2×#179848682
#225815032
#225813482
#225813432
#225813352
C4×#145557692
C2×#124×C1392
#3153139