Finite Group Databasebeta

← #31807471

Subgroups — #31807471

Order 17792.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#22581753C211yesmaximal, characteristic, complemented
2#22581464C212yesmaximal, complemented
3#22580969C212yesmaximal, complemented
4#22580710C211yesmaximal, characteristic, complemented
5#407×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2212yes—
7#17984875—22no—
8#17984870—22no—
9#17984864—22no—
10#17984825—22no—
11#17984821—22no—
12#17984816—22no—
13#17984811—22no—
14C4×C22⋊D139—24no—
15#17984801C2212yes—
16#17984768—24no—
17C23×C4×C139C2211yescharacteristic
18C2×M16×C139C2211yescharacteristic
19C2×M16×C139C2211yescharacteristic
20C22⋊C8×C139—22no—
21#14555785—22no—
22#14555785—22no—
23#14555785—22no—
24#14555785—22no—
25C2×Dic278D412yescomplemented
26C2×D556D412yescomplemented
27C2×C22⋊D139—24no—
28C2×C22⋊D139—22no—
29C2×C4×D139—22no—
30Dic556—22no—
31#14555774—24no—
32D1112—22no—
33C4⋊Dic139—22no—
34Dic139⋊C4—24no—
35C22⋊Dic139—24no—
36C22⋊Dic139—22no—
37(C2×D139)⋊C4—24no—
38C4×Dic139D414yescomplemented
39C24×C139D411yescharacteristic
40C22×C4×C139—22no—
41C22×C4×C139—22no—
42C22×C4×C139—21no—
43C22×C4×C139—21no—
44C22×C4×C139D411yescharacteristic
45C22×C4×C139C2311yescharacteristic
46M16×C139—22no—
47M16×C139—22no—
48C2×C8×C139—21no—
49C2×C8×C139D412yescomplemented
50C22×D139—22no—
51Dic278—22no—
52Dic278—22no—
53D556—22no—
54D556—22no—
55C22⋊D139—48no—
56C22⋊D139—42no—
57C22⋊D139—42no—
58C2×Dic139—24no—
59C2×Dic139—22no—
60C4×D139—42no—
61C4×D139—42no—
62C23×C139—22no—
63C23×C139—21no—
64C23×C139—42no—
65C23×C139C2×D411yescharacteristic
66C2×C4×C139—22no—
67C2×C4×C139—21no—
68C2×C4×C139—41no—
69C2×C4×C139—42no—
70C2×C4×C139—41no—
71C2×C4×C139C2×D412yes—
72C2×C4×C139C2×D412yes—
73C2×C4×C139C2×D411yescharacteristic
74C2×C4×C139#4111yescharacteristic
75C8×C139—22no—
76C8×C139—41no—
77C22×C139—22no—
78C22×C139—24no—
79C22×C139—41no—
80C22×C139—42no—
81C22×C139—41no—
82C22×C139—41no—
83C22×C139#12012yes—
84C22×C139#12111yescharacteristic
85C2×D139—44no—
86C2×D139—42no—
87C4×C139—41no—
88C4×C139#12011yescharacteristic
89C4×C139#12112yes—
90C4×C139#12711yescharacteristic
91Dic139—44no—
92Dic139—42no—
93C2×C139—22no—
94C2×C139—21no—
95C2×C139—42no—
96C2×C139#39211yescharacteristic
97D139—82no—
98C139#201011yescharacteristic, complemented, Sylow
99#2010—1391nomaximal, Sylow
100#575—1391no—
101#525—1392no—
102#421—1392no—
103#407D13911yescharacteristic, complemented
104H(3,ℤ/4)—1391no—
105C2×#41—1392no—
106C23×C4C2×D13911yescharacteristic
107#137—2782no—
108AGL(1,ℤ/8)—2782no—
109#135—2782no—
110C2×M16C2×D13911yescharacteristic
111C2×M16C2×D13911yescharacteristic
112#123—2782no—
113C22⋊Q8—2782no—
114#121—2782no—
115#120—2782no—
116C4×D4—2784no—
117#117—1392no—
118#104—2784no—
119C22⋊C8—22no—
120C24D55611yescharacteristic
121#41—2782no—
122#41—2782no—
123#41—2782no—
124#41—2782no—
125C2×Q8—1392no—
126C2×D4—2784no—
127C2×D4—2782no—
128C2×D4—1392no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—2782no—
134C22×C4D55611yescharacteristic
135C22×C4C22×D13911yescharacteristic
136Q16—2782no—
137SD16—2784no—
138D8—2782no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D13912yescomplemented
143C4⋊C4—2784no—
144C4⋊C4—2782no—
145C22⋊C4—2784no—
146C22⋊C4—2784no—
147C22⋊C4—2782no—
148C42—1394no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—2782no—
153C23C2×D55611yescharacteristic
154Q8—2782no—
155Q8—2782no—
156D4—2782no—
157D4—2782no—
158D4—5568no—
159D4—5562no—
160D4—5562no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—2784no—
167C2×C4—2782no—
168C2×C4—5562no—
169C2×C4—5562no—
170C2×C4D4×D13912yes—
171C2×C4D4×D13912yes—
172C2×C4C2×C22⋊D13911yescharacteristic
173C2×C4#1455578511yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—5564no—
183C22—5562no—
184C22#1798481212yes—
185C22#1798481611yescharacteristic
186C4—41no—
187C4—5564no—
188C4—5562no—
189C4#1798481011yescharacteristic
190C4#1798481512yes—
191C4#1798483811yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—11122no—
196C2#2258086211yescharacteristic
subgroupG/H
centerC4#17984838
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#407×C139C2
socleC2×C139#392
hypercenter#407D139
hypocenterC139#2010
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #22581753C2semidirect
2. #22581464C2semidirect
3. #22580969C2semidirect
4. #22580710C2semidirect
5. #407×C139C2semidirect
25. C2×Dic278D4semidirect
26. C2×D556D4semidirect
38. C4×Dic139D4semidirect
49. C2×C8×C139D4semidirect
98. C139#2010semidirect
103. #407D139semidirect
142. C2×C8C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225817532
#225814642
#225809692
#225807102
#407×C1392
#2010139