Finite Group Databasebeta

← #31805735

Subgroups — #31805735

Order 17792.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#22581707C211yesmaximal, characteristic
2#22581359C211yesmaximal, characteristic, complemented
3#22581315C211yesmaximal, characteristic
4#22580695C211yesmaximal, characteristic, complemented
5#22580694C211yesmaximal, characteristic, complemented
6#22580692C211yesmaximal, characteristic
7#491×C139C211yesmaximal, characteristic, complemented
8#17984841—21no—
9#17984837—21no—
10#17984837—21no—
11#17984834C2211yescharacteristic
12#17984830C2211yescharacteristic
13#17984827—21no—
14#17984822—21no—
15#17984820—21no—
16#17984775—21no—
17#17984773—21no—
18#17984765—21no—
19#17984762—21no—
20#17984753C2211yescharacteristic
21#17984753C2211yescharacteristic
22C4⋊Q8×C139C2211yescharacteristic
23#125×C139C2211yescharacteristic
24#103×C139—21no—
25#103×C139—21no—
26#97×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278D411yescharacteristic
29C2×D556D411yescharacteristic
30C2×C4×D139—21no—
31C2×C139⋊C8—21no—
32C2×C139⋊C8—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139D411yescharacteristic
35C4⋊Dic139D411yescharacteristic
36Dic139⋊C4—21no—
37Dic139⋊C4—21no—
38Dic139⋊C4—21no—
39(C2×D139)⋊C4—21no—
40(C2×D139)⋊C4—21no—
41(C2×D139)⋊C4—21no—
42(C2×D139)⋊C4—21no—
43(C2×D139)⋊C4—21no—
44C4×Dic139—21no—
45C2×Q8×C139—21no—
46C2×C8×C139—21no—
47C4⋊C4×C139—21no—
48C4⋊C4×C139—21no—
49C4⋊C4×C139—21no—
50C4⋊C4×C139—21no—
51C4⋊C4×C139D411yescharacteristic
52C4⋊C4×C139D411yescharacteristic
53C42×C139C2311yescharacteristic
54C22×D139—21no—
55Dic278—41no—
56Dic278—81no—
57D556—41no—
58C2×Dic139—21no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C4×D139—81no—
62C139⋊C8—22no—
63C139⋊C8—41no—
64Q8×C139—42no—
65C2×C4×C139—21no—
66C2×C4×C139—21no—
67C2×C4×C139—41no—
68C2×C4×C139C2×D411yescharacteristic
69C2×C4×C139C2×D411yescharacteristic
70C2×C4×C139C2×D411yescharacteristic
71C8×C139—41no—
72C22×C139#12011yescharacteristic
73C2×D139—41no—
74C2×D139—41no—
75C2×D139—41no—
76C4×C139—21no—
77C4×C139—21no—
78C4×C139—21no—
79C4×C139—41no—
80C4×C139—41no—
81C4×C139—81no—
82Dic139—41no—
83Dic139—41no—
84Dic139—41no—
85C2×C139#45411yescharacteristic
86C2×C139#45511yescharacteristic
87C2×C139#45611yescharacteristic
88D139—81no—
89C139#166411yescharacteristic, complemented, Sylow
90#1664—1391nomaximal, Sylow
91#563—1391no—
92#501—1391no—
93#491D13911yescharacteristic, complemented
94#489—1391no—
95#330—1391no—
96#330—1391no—
97#329—1391no—
98C4⋊Q8—2781no—
99C4⋊Q8C2×D13911yescharacteristic
100#126—2781no—
101#126—2781no—
102#125—1391no—
103#125C2×D13911yescharacteristic
104#124—1391no—
105#123—2781no—
106C22⋊Q8—2781no—
107C22⋊Q8—2781no—
108#107—2781no—
109#106—2781no—
110#103—21no—
111#103—21no—
112#103—2781no—
113#102—2781no—
114#97—1391no—
115#97—1391no—
116#97C2×D13911yescharacteristic
117C2×Q8—21no—
118C2×Q8—2781no—
119C2×Q8—1391no—
120C2×D4—1391no—
121C22×C4—2781no—
122C2×C8—21no—
123C2×C8—2781no—
124C2×C8—2781no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2781no—
130C4⋊C4—2781no—
131C4⋊C4—2781no—
132C4⋊C4—2781no—
133C4⋊C4—1391no—
134C4⋊C4—1391no—
135C4⋊C4C22⋊D13911yescharacteristic
136C4⋊C4C22⋊D13911yescharacteristic
137C22⋊C4—2781no—
138C22⋊C4—2781no—
139C22⋊C4—2781no—
140C22⋊C4—2781no—
141C22⋊C4—2781no—
142C42—2781no—
143C42C22×D13911yescharacteristic
144C23—2781no—
145Q8—42no—
146Q8—5561no—
147Q8—11121no—
148D4—5561no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—2781no—
153C2×C4—2781no—
154C2×C4—2781no—
155C2×C4—11121no—
156C2×C4D4×D13911yescharacteristic
157C2×C4D4×D13911yescharacteristic
158C2×C4C2×C22⋊D13911yescharacteristic
159C8—41no—
160C8—2782no—
161C8—5561no—
162C22—5561no—
163C22—5561no—
164C22—5561no—
165C22#1798481011yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—5561no—
173C4—5561no—
174C4—5561no—
175C2—11121no—
176C2#2258112511yescharacteristic
177C2#2258112911yescharacteristic
178C2#2258113411yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#491×C139C2
socleC22×C139#120
prime radicalC2×D556D4
hypercenter#491D139
hypocenterC139#1664
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #22581359C2semidirect
4. #22580695C2semidirect
5. #22580694C2semidirect
7. #491×C139C2semidirect
89. C139#1664semidirect
93. #491D139semidirect

Maximal subgroups

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

subgroupindex
#225817072
#225813592
#225813152
#225806952
#225806942
#225806922
#491×C1392
#1664139