Finite Group Databasebeta

← #31807628

Subgroups — #31807628

Order 17792.

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

normal subgroups only

This group has 306 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#384×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×C139—22no—
15C2×C4⋊C4×C139C2211yescharacteristic
16C2×C4⋊C4×C139C2211yescharacteristic
17C2×C42×C139C2211yescharacteristic
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—
38C4⋊C4×C139—44no—
39C42×C139—21no—
40C42×C139D412yescomplemented
41C22×D139—22no—
42Dic278—22no—
43Dic278—22no—
44D556—22no—
45D556—22no—
46D556—82no—
47C22⋊D139—42no—
48C22⋊D139—42no—
49C2×Dic139—22no—
50C4×D139—42no—
51C4×D139—42no—
52C139⋊C8—42no—
53C23×C139C2×D411yescharacteristic
54C2×C4×C139—22no—
55C2×C4×C139—22no—
56C2×C4×C139—22no—
57C2×C4×C139—22no—
58C2×C4×C139—42no—
59C2×C4×C139—42no—
60C2×C4×C139—41no—
61C2×C4×C139C2×D412yes—
62C2×C4×C139C2×D411yescharacteristic
63C2×C4×C139#4111yescharacteristic
64C2×C4×C139#4112yes—
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—24no—
74C4×C139—42no—
75C4×C139—81no—
76C4×C139#12112yes—
77C4×C139#12312yes—
78Dic139—42no—
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#384D13911yescharacteristic, complemented
91#343—1391no—
92C2×#41—1392no—
93C2×M16—1392no—
94C22⋊Q8—2782no—
95#121—2782no—
96#121—2782no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4C2×D13911yescharacteristic
99C2×C4⋊C4C2×D13911yescharacteristic
100C2×C42C2×D13911yescharacteristic
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—21no—
113C22×C4—21no—
114C22×C4—2782no—
115C22×C4C22⋊D13912yes—
116C22×C4C22×D13911yescharacteristic
117M16—2782no—
118M16—2782no—
119C2×C8—2782no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—44no—
123C4⋊C4—2782no—
124C22⋊C4—2784no—
125C42—21no—
126C42D55612yescomplemented
127C23—2782no—
128C23C2×C22⋊D13911yescharacteristic
129Q8—2782no—
130Q8—2782no—
131D4—2782no—
132D4—2782no—
133D4—5562no—
134D4—5562no—
135D4—11122no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—2782no—
144C2×C4—5562no—
145C2×C4—5562no—
146C2×C4D4×D13912yes—
147C2×C4C2×D55611yescharacteristic
148C2×C4#1455578511yescharacteristic
149C2×C4#1455578612yes—
150C8—5562no—
151C22—21no—
152C22—21no—
153C22—5562no—
154C22—5562no—
155C22—5562no—
156C22#1798481011yescharacteristic
157C22#1798481611yescharacteristic
158C22#1798483111yescharacteristic
159C4—24no—
160C4—42no—
161C4—81no—
162C4—5562no—
163C4#1798481712yes—
164C4#1798482712yes—
165C2—21no—
166C2—21no—
167C2—11122no—
168C2#2258087011yescharacteristic
169C2#2258112011yescharacteristic
170C2#2258113511yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#384×C139C2
socleC22×C139#120
prime radical#22581534C2
hypercenter#384D139
hypocenterC139#2039
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#17984770C2semidirect
3. #22580952C2semidirect
4. #22580722C2semidirect
5. #384×C139C2semidirect
40. C42×C139D4semidirect
85. C139#2039semidirect
90. #384D139semidirect
126. 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
#384×C1392
#2039139