Finite Group Databasebeta

← #31807629

Subgroups — #31807629

Order 17792.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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×#17984768C212yesmaximal, complemented
3#22580955C212yesmaximal, complemented
4#22580822C211yesmaximal, characteristic, complemented
5#343×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2212yes—
7#17984822—22no—
8#17984817—22no—
9#17984816—22no—
10C2×C4⋊Dic139C2211yescharacteristic
11C2×Dic139⋊C4—22no—
12C2×C4×Dic139C2211yescharacteristic
13#17984768—24no—
14#17984767—22no—
15#17984764—22no—
16C2×M16×C139C2212yes—
17C2×C4⋊C4×C139C2211yescharacteristic
18#14555785—22no—
19#14555785—22no—
20#14555785—22no—
21#14555785—22no—
22C2×Dic278D412yes—
23C2×D556—22no—
24C2×D556D412yes—
25C2×C22⋊D139—22no—
26C22×Dic139—21no—
27C22×Dic139—21no—
28C2×C4×D139—22no—
29C4⋊Dic139—22no—
30C4⋊Dic139—22no—
31Dic139⋊C4—44no—
32(C2×D139)⋊C4—24no—
33C4×Dic139—21no—
34C4×Dic139D412yescomplemented
35C22×C4×C139D412yes—
36C22×C4×C139C2311yescharacteristic
37M16×C139—22no—
38M16×C139—22no—
39C2×C8×C139—22no—
40C4⋊C4×C139—22no—
41C22×D139—22no—
42Dic278—22no—
43Dic278—22no—
44D556—22no—
45D556—22no—
46D556—82no—
47C22⋊D139—42no—
48C22⋊D139—42no—
49C2×Dic139—22no—
50C2×Dic139—22no—
51C2×Dic139—22no—
52C2×Dic139—22no—
53C2×Dic139—42no—
54C2×Dic139—41no—
55C4×D139—42no—
56C4×D139—42no—
57C23×C139C2×D411yescharacteristic
58C2×C4×C139—22no—
59C2×C4×C139—42no—
60C2×C4×C139C2×D411yescharacteristic
61C2×C4×C139C2×D412yes—
62C2×C4×C139#4112yes—
63C2×C4×C139#4111yescharacteristic
64C8×C139—42no—
65C22×C139—21no—
66C22×C139—21no—
67C22×C139#12011yescharacteristic
68C22×C139#12111yescharacteristic
69C22×C139#12411yescharacteristic
70C2×D139—42no—
71C2×D139—42no—
72C2×D139—42no—
73C4×C139—42no—
74C4×C139#12112yes—
75C4×C139#12312yes—
76Dic139—24no—
77Dic139—42no—
78Dic139—81no—
79C2×C139—21no—
80C2×C139—21no—
81C2×C139#39411yescharacteristic
82C2×C139#45311yescharacteristic
83C2×C139#45611yescharacteristic
84D139—82no—
85C139#203911yescharacteristic, complemented, Sylow
86#2039—1391nomaximal, Sylow
87#537—1391no—
88C2×#104—1392no—
89#417—1392no—
90#384—1391no—
91#343D13911yescharacteristic, complemented
92C2×#41—1392no—
93C2×M16C2×D13912yes—
94C22⋊Q8—2782no—
95#121—2782no—
96#121—2782no—
97C2×C4⋊C4—2782no—
98C2×C4⋊C4—1391no—
99C2×C4⋊C4C2×D13911yescharacteristic
100C2×C42—1391no—
101#104—2784no—
102#103—2782no—
103#102—2782no—
104#41—2782no—
105#41—2782no—
106#41—2782no—
107#41—2782no—
108C2×Q8—1392no—
109C2×D4—2782no—
110C2×D4—2782no—
111C2×D4—1392no—
112C22×C4—2781no—
113C22×C4—2782no—
114C22×C4—2781no—
115C22×C4D55612yes—
116C22×C4C22×D13911yescharacteristic
117M16—22no—
118M16—22no—
119C2×C8—22no—
120C4⋊C4—22no—
121C4⋊C4—2782no—
122C4⋊C4—2782no—
123C4⋊C4—5564no—
124C22⋊C4—2784no—
125C42—2781no—
126C42—1392no—
127C23—2782no—
128C23C2×D55611yescharacteristic
129Q8—2782no—
130Q8—2782no—
131D4—2782no—
132D4—2782no—
133D4—5562no—
134D4—5562no—
135D4—11122no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—2782no—
139C2×C4—2782no—
140C2×C4—2782no—
141C2×C4—2782no—
142C2×C4—5562no—
143C2×C4—5562no—
144C2×C4—5562no—
145C2×C4—5561no—
146C2×C4D4×D13911yescharacteristic
147C2×C4D4×D13912yes—
148C2×C4#1455578512yes—
149C2×C4#1455578611yescharacteristic
150C8—42no—
151C22—21no—
152C22—21no—
153C22—5562no—
154C22—5562no—
155C22—5562no—
156C22#1798481211yescharacteristic
157C22#1798481711yescharacteristic
158C22#1798483011yescharacteristic
159C4—42no—
160C4—2784no—
161C4—5562no—
162C4—11121no—
163C4#1798481512yes—
164C4#1798482712yes—
165C2—21no—
166C2—21no—
167C2—11122no—
168C2#2258087111yescharacteristic
169C2#2258112311yescharacteristic
170C2#2258113811yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#343×C139C2
socleC22×C139#120
prime radical#22581534C2
hypercenter#343D139
hypocenterC139#2039
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#17984768C2semidirect
3. #22580955C2semidirect
4. #22580822C2semidirect
5. #343×C139C2semidirect
34. C4×Dic139D4semidirect
85. C139#2039semidirect
91. #343D139semidirect

Maximal subgroups

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

subgroupindex
#225815342
C2×#179847682
#225809552
#225808222
#343×C1392
#2039139