Finite Group Databasebeta

← #31807633

Subgroups — #31807633

Order 17792.

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

normal subgroups only

This group has 290 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#22581534C211yesmaximal, characteristic
2C2×#17984770C212yesmaximal, complemented
3#22580952C212yesmaximal, complemented
4#22580722C211yesmaximal, characteristic, complemented
5#382×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2212yes—
7C2×#14555769C2212yes—
8#17984822—22no—
9#17984817—22no—
10#17984816—22no—
11#17984770—24no—
12#17984765—22no—
13#17984762—22no—
14C2×C4⋊C4×C139C2211yescharacteristic
15C2×C4⋊C4×C139C2211yescharacteristic
16C2×C42×C139C2211yescharacteristic
17#95×C139—22no—
18#14555785—22no—
19#14555785—22no—
20#14555785—22no—
21#14555785—22no—
22C2×Dic278D412yes—
23C2×D556—22no—
24C2×D556D412yes—
25C2×C22⋊D139—22no—
26C2×C4×D139—22no—
27#14555769—22no—
28#14555769—22no—
29C2×C139⋊C8—22no—
30C4⋊Dic139—22no—
31(C2×D139)⋊C4—24no—
32C22×C4×C139—21no—
33C22×C4×C139—21no—
34C22×C4×C139D412yes—
35C22×C4×C139C2311yescharacteristic
36C4⋊C4×C139—22no—
37C4⋊C4×C139—22no—
38C42×C139—21no—
39C42×C139D412yescomplemented
40C22×D139—22no—
41Dic278—22no—
42Dic278—22no—
43D556—22no—
44D556—22no—
45D556—82no—
46C22⋊D139—42no—
47C22⋊D139—42no—
48C2×Dic139—22no—
49C4×D139—42no—
50C4×D139—42no—
51C139⋊C8—42no—
52C23×C139C2×D411yescharacteristic
53C2×C4×C139—22no—
54C2×C4×C139—22no—
55C2×C4×C139—41no—
56C2×C4×C139—41no—
57C2×C4×C139—42no—
58C2×C4×C139—42no—
59C2×C4×C139—41no—
60C2×C4×C139C2×D412yes—
61C2×C4×C139C2×D411yescharacteristic
62C2×C4×C139#4111yescharacteristic
63C2×C4×C139#4112yes—
64C22×C139—21no—
65C22×C139—21no—
66C22×C139#12011yescharacteristic
67C22×C139#12111yescharacteristic
68C22×C139#12411yescharacteristic
69C2×D139—42no—
70C2×D139—42no—
71C2×D139—42no—
72C4×C139—42no—
73C4×C139—42no—
74C4×C139—81no—
75C4×C139#12112yes—
76C4×C139#12312yes—
77Dic139—42no—
78C2×C139—21no—
79C2×C139—21no—
80C2×C139#39411yescharacteristic
81C2×C139#45411yescharacteristic
82C2×C139#45511yescharacteristic
83D139—82no—
84C139#204011yescharacteristic, complemented, Sylow
85#2040—1391nomaximal, Sylow
86#537—1391no—
87C2×#104—1392no—
88#417—1392no—
89#382D13911yescharacteristic, complemented
90#343—1391no—
91C2×#41—1392no—
92C2×M16—1392no—
93C22⋊Q8—2782no—
94#121—2782no—
95#121—2782no—
96C2×C4⋊C4C2×D13911yescharacteristic
97C2×C4⋊C4C2×D13911yescharacteristic
98C2×C42C2×D13911yescharacteristic
99#104—2784no—
100#103—2782no—
101#102—2782no—
102#95—22no—
103#41—2782no—
104#41—2782no—
105#41—2782no—
106#41—2782no—
107C2×Q8—1392no—
108C2×D4—2782no—
109C2×D4—2782no—
110C2×D4—1392no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—2782no—
114C22×C4C22⋊D13912yes—
115C22×C4C22×D13911yescharacteristic
116M16—2782no—
117M16—2782no—
118C2×C8—2782no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—2782no—
122C22⋊C4—2784no—
123C42—21no—
124C42D55612yescomplemented
125C23—2782no—
126C23C2×C22⋊D13911yescharacteristic
127Q8—2782no—
128Q8—2782no—
129D4—2782no—
130D4—2782no—
131D4—5562no—
132D4—5562no—
133D4—11122no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—2782no—
142C2×C4—5562no—
143C2×C4—5562no—
144C2×C4D4×D13912yes—
145C2×C4C2×D55611yescharacteristic
146C2×C4#1455578511yescharacteristic
147C2×C4#1455578612yes—
148C8—5562no—
149C22—21no—
150C22—21no—
151C22—5562no—
152C22—5562no—
153C22—5562no—
154C22#1798481011yescharacteristic
155C22#1798481611yescharacteristic
156C22#1798483111yescharacteristic
157C4—42no—
158C4—42no—
159C4—81no—
160C4—5562no—
161C4#1798481712yes—
162C4#1798482712yes—
163C2—21no—
164C2—21no—
165C2—11122no—
166C2#2258087011yescharacteristic
167C2#2258112511yescharacteristic
168C2#2258113011yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#382×C139C2
socleC22×C139#120
prime radical#22581534C2
hypercenter#382D139
hypocenterC139#2040
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#17984770C2semidirect
3. #22580952C2semidirect
4. #22580722C2semidirect
5. #382×C139C2semidirect
39. C42×C139D4semidirect
84. C139#2040semidirect
89. #382D139semidirect
124. C42D556semidirect

Maximal subgroups

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

subgroupindex
#225815342
C2×#179847702
#225809522
#225807222
#382×C1392
#2040139