Finite Group Databasebeta

← #31806321

Subgroups — #31806321

Order 17792.

612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#14555785C211yesmaximal, characteristic
2C2×#17984756C214yesmaximal, complemented
3#22580816C211yesmaximal, characteristic, complemented
4#381×C139C211yesmaximal, characteristic, complemented
5C2×#14555785—28no—
6C2×#14555785—22no—
7C2×#14555785—22no—
8C22×Dic278C411yescharacteristic, complemented
9C22×D556C411yescharacteristic, complemented
10C22×C22⋊D139C2212yes—
11C22×C4×D139C412yescomplemented
12C2×C22⋊Dic139C2212yes—
13#17984756—28no—
14C139⋊#95—22no—
15C23×C4×C139C2211yescharacteristic
16C2×C22⋊C4×C139C2212yes—
17#95×C139—22no—
18C23×D139C2×C412yes—
19#14555785—216no—
20#14555785—216no—
21C2×Dic278—24no—
22C2×Dic278—22no—
23C2×D556—24no—
24C2×D556—22no—
25C2×C22⋊D139—24no—
26C2×C22⋊D139—22no—
27C2×C22⋊D139—22no—
28C2×C22⋊D139D418yes—
29C22×Dic139—22no—
30C22×Dic139C2×C412yes—
31C2×C4×D139—24no—
32C2×C4×D139—24no—
33C2×C4×D139—24no—
34C22⋊Dic139—24no—
35C24×C139C2311yescharacteristic
36C22×C4×C139—24no—
37C22×C4×C139—22no—
38C22×C4×C139C2×C411yescharacteristic
39C22×C4×C139C2×C411yescharacteristic
40C22×C4×C139D412yes—
41C22×C4×C139D412yes—
42C22⋊C4×C139—24no—
43C22×D139—22no—
44C22×D139—22no—
45C22×D139—44no—
46C22×D139C22⋊C414yes—
47Dic278—28no—
48D556—28no—
49C22⋊D139—28no—
50C22⋊D139—28no—
51C2×Dic139—22no—
52C2×Dic139—22no—
53C2×Dic139—44no—
54C2×Dic139—42no—
55C2×Dic139C22⋊C414yes—
56C4×D139—216no—
57C23×C139—42no—
58C23×C139C22×C411yescharacteristic
59C23×C139C2×D414yes—
60C23×C139C2×D411yescharacteristic
61C23×C139C2×D411yescharacteristic
62C2×C4×C139—22no—
63C2×C4×C139—22no—
64C2×C4×C139—24no—
65C2×C4×C139—24no—
66C2×C4×C139—44no—
67C2×C4×C139—42no—
68C2×C4×C139C22⋊C412yes—
69C2×C4×C139C22⋊C412yes—
70C22×C139—22no—
71C22×C139—22no—
72C22×C139—22no—
73C22×C139—44no—
74C22×C139C2×C22⋊C412yes—
75C22×C139C2×C22⋊C411yescharacteristic
76C22×C139#12012yes—
77C22×C139#12012yes—
78C2×D139—24no—
79C2×D139—44no—
80C2×D139—44no—
81C2×D139—44no—
82C4×C139—22no—
83C4×C139—22no—
84C4×C139—82no—
85Dic139—24no—
86Dic139—82no—
87C2×C139—22no—
88C2×C139—22no—
89C2×C139—22no—
90C2×C139#37911yescharacteristic
91C2×C139#41012yes—
92D139—44no—
93C139#178211yescharacteristic, complemented, Sylow
94#1782—1391nomaximal, Sylow
95C22×#41—1391no—
96C2×#99—1394no—
97#381—1391no—
98#381D13911yescharacteristic, complemented
99C2×#41—2788no—
100C2×#41—2782no—
101C2×#41—2782no—
102C22×Q8—1391no—
103C22×D4—1392no—
104C22×D4—1391no—
105C23×C4—1392no—
106C23×C4C2×D13911yescharacteristic
107C2×C22⋊C4—1392no—
108C2×C22⋊C4C2×D13912yes—
109#99—2788no—
110#95—22no—
111#95—2782no—
112C24—1392no—
113C24C22×D13911yescharacteristic
114#41—27816no—
115#41—27816no—
116C2×Q8—2784no—
117C2×Q8—2782no—
118C2×D4—2784no—
119C2×D4—2784no—
120C2×D4—2782no—
121C2×D4—2782no—
122C2×D4—2782no—
123C2×D4—1398no—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—2784no—
127C22×C4—2784no—
128C22×C4—2784no—
129C22×C4—2782no—
130C22×C4—1392no—
131C22×C4C4×D13911yescharacteristic
132C22×C4C4×D13911yescharacteristic
133C22×C4C22⋊D13912yes—
134C22×C4D55612yes—
135C22⋊C4—24no—
136C22⋊C4—2784no—
137C23—42no—
138C23—2782no—
139C23—2782no—
140C23—5564no—
141C23—1394no—
142C23C2×C4×D13911yescharacteristic
143C23D4×D13914yes—
144C23C2×C22⋊D13911yescharacteristic
145C23C2×D55611yescharacteristic
146Q8—2788no—
147D4—2788no—
148D4—2788no—
149D4—2788no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—44no—
155C2×C4—42no—
156C2×C4—27816no—
157C2×C4—2782no—
158C2×C4—2782no—
159C2×C4—5564no—
160C2×C4—5562no—
161C2×C4—1394no—
162C2×C4(C2×D139)⋊C412yes—
163C2×C4(C2×D139)⋊C412yes—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—2784no—
169C22—5564no—
170C22—5564no—
171C22—5564no—
172C22C22⋊C4×D13912yes—
173C22C2×(C2×D139)⋊C411yescharacteristic
174C22#1798481012yes—
175C22#1798481212yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—2784no—
180C4—11122no—
181C2—22no—
182C2—22no—
183C2—22no—
184C2—5564no—
185C2#2258080811yescharacteristic
186C2#2258092612yes—
subgroupG/H
centerC22C2×(C2×D139)⋊C4
commutatorC23×C139C22×C4
FrattiniC24C22×D139
Fitting#381×C139C2
socleC22×C139C2×C22⋊C4
prime radicalC22×#14555785C2
cosocleC24×C139C23
hypercenter#381D139
hypocenterC139#1782
LCSG ▷ C23×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#17984756C2semidirect
3. #22580816C2semidirect
4. #381×C139C2semidirect
8. C22×Dic278C4semidirect
9. C22×D556C4semidirect
11. C22×C4×D139C4semidirect
93. C139#1782semidirect
98. #381D139semidirect

Maximal subgroups

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

subgroupindex
C22×#145557852
C2×#179847562
#225808162
#381×C1392
#1782139