Finite Group Databasebeta

← #31808381

Subgroups — #31808381

Order 17792.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#22581766C211yesmaximal, characteristic
2#22581394C211yesmaximal, characteristic, complemented
3#22581225C211yesmaximal, characteristic, complemented
4#22580769C211yesmaximal, characteristic, complemented
5#22580761C211yesmaximal, characteristic, complemented
6#22580736C211yesmaximal, characteristic, complemented
7C2×Q32×C139C211yesmaximal, characteristic, complemented
8#17984890—21no—
9#17984874—22no—
10#17984873—21no—
11#17984873—21no—
12#17984865—21no—
13#17984864C2211yescharacteristic
14Q16×D139—21no—
15#17984848C2211yescharacteristic
16#17984788—21no—
17#17984785—21no—
18#17984782C2211yescharacteristic
19#17984778C2211yescharacteristic
20#17984761—21no—
21C2×Q16×C139C2211yescharacteristic
22C2×Q16×C139C2211yescharacteristic
23Q32×C139—22no—
24C2×C16×C139C2211yescharacteristic
25#14555786—22no—
26#14555786—41no—
27#14555785—21no—
28#14555785—42no—
29#14555785D411yescharacteristic
30Q8×D139—22no—
31Q8×D139—41no—
32Dic556D411yescharacteristic
33#14555775—22no—
34#14555775—41no—
35#14555774—21no—
36#14555772—22no—
37#14555772—41no—
38D1112D411yescharacteristic
39#14555769—21no—
40#14555769D411yescharacteristic
41#14555768—21no—
42C8×D139—21no—
43C139⋊C16—21no—
44C2×Q8×C139—21no—
45C2×Q8×C139—21no—
46Q16×C139—21no—
47Q16×C139—21no—
48Q16×C139—21no—
49Q16×C139D412yes—
50C2×C8×C139C2311yescharacteristic
51C16×C139—21no—
52Dic278—21no—
53Dic278—42no—
54Dic278D811yescharacteristic
55D556—21no—
56D556—42no—
57D556D811yescharacteristic
58C22⋊D139—21no—
59C22⋊D139—41no—
60C4×D139—21no—
61C4×D139—42no—
62C4×D139—42no—
63C4×D139—41no—
64C139⋊C8—21no—
65C139⋊C8—41no—
66Q8×C139—22no—
67Q8×C139—41no—
68Q8×C139—41no—
69Q8×C139—41no—
70C2×C4×C139—41no—
71C2×C4×C139—41no—
72C2×C4×C139C2×D411yescharacteristic
73C8×C139C2×D411yescharacteristic
74C8×C139C2×D411yescharacteristic
75C22×C139AGL(1,ℤ/8)11yescharacteristic
76C2×D139—21no—
77C2×D139—41no—
78C4×C139—42no—
79C4×C139—81no—
80C4×C139#12011yescharacteristic
81C4×C139C2×D811yescharacteristic
82Dic139—21no—
83Dic139—41no—
84C2×C139—21no—
85C2×C139#44711yescharacteristic
86D139—41no—
87D139—81no—
88C139#219511yescharacteristic, complemented, Sylow
89#2195—1391nomaximal, Sylow
90#578—1391no—
91#510—1391no—
92C2×Q32D13911yescharacteristic, complemented
93#473—1391no—
94#362—1391no—
95#359—1391no—
96#350—1391no—
972−1+4—2781no—
98#137—2782no—
99#137—2781no—
100#137—2781no—
101#135—2781no—
102#135—1391no—
103C2×Q16—2781no—
104C2×Q16C2×D13911yescharacteristic
105C2×Q16C2×D13911yescharacteristic
106#131—1391no—
107Q32—22no—
108Q32—2781no—
109SD32—2781no—
110M32—1391no—
111C2×C16C2×D13911yescharacteristic
112#108—1391no—
113#101—2781no—
114#41—2782no—
115#41—2781no—
116#41—5562no—
117#41—5561no—
118#41—1391no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—2782no—
122C2×Q8—5561no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—2782no—
127Q16—5561no—
128Q16—1391no—
129Q16C22⋊D13912yes—
130SD16—2782no—
131SD16—2781no—
132SD16—5561no—
133D8—1391no—
134M16—2781no—
135M16—2781no—
136M16—1391no—
137C2×C8—2781no—
138C2×C8C22×D13911yescharacteristic
139C16—21no—
140C16—2781no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—2781no—
146Q8—5562no—
147Q8—1391no—
148D4—2781no—
149D4—2781no—
150D4—5562no—
151D4—5561no—
152D4—1391no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—2781no—
156C2×C4—5562no—
157C2×C4—5562no—
158C2×C4—5561no—
159C2×C4D4×D13911yescharacteristic
160C8—2781no—
161C8—5561no—
162C8D4×D13911yescharacteristic
163C8C2×C22⋊D13911yescharacteristic
164C22—2781no—
165C22—5561no—
166C22#1798486611yescharacteristic
167C4—42no—
168C4—81no—
169C4—2781no—
170C4—5561no—
171C4#1798481011yescharacteristic
172C4D8×D13911yescharacteristic
173C2—21no—
174C2—5561no—
175C2—11121no—
176C2#2258108511yescharacteristic
subgroupG/H
centerC2#22581085
commutator, cosocleC2×C8×C139C23
FrattiniC2×C8C22×D139
FittingC2×Q32×C139C2
socleC2×C139#447
prime radical#22581766C2
hypercenterC2×Q32D139
hypocenterC139#2195
LCSG ▷ C2×C8×C139 ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #22581394C2semidirect
3. #22581225C2semidirect
4. #22580769C2semidirect
5. #22580761C2semidirect
6. #22580736C2semidirect
7. C2×Q32×C139C2semidirect
88. C139#2195semidirect
92. C2×Q32D139semidirect

Maximal subgroups

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

subgroupindex
#225817662
#225813942
#225812252
#225807692
#225807612
#225807362
C2×Q32×C1392
#2195139