Finite Group Databasebeta

← #31805587

Subgroups — #31805587

Order 17792.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#22581689C211yesmaximal, characteristic
2#22581235C211yesmaximal, characteristic, complemented
3#22581160C211yesmaximal, characteristic, complemented
4#22580697C211yesmaximal, characteristic
5#22580685C211yesmaximal, characteristic, complemented
6#22580685C211yesmaximal, characteristic, complemented
7#486×C139C211yesmaximal, characteristic
8C2×#14555775—21no—
9#17984829—21no—
10#17984829—21no—
11#17984823—22no—
12C4×Dic278C2211yescharacteristic
13C4×Dic278C2211yescharacteristic
14D4×Dic139—21no—
15D4×Dic139—21no—
16#17984773—21no—
17C4⋊(C139⋊C8)C2211yescharacteristic
18C4⋊(C139⋊C8)C2211yescharacteristic
19#17984766—21no—
20#17984765—21no—
21C4⋊Q8×C139C2211yescharacteristic
22#127×C139C2211yescharacteristic
23#102×C139—22no—
24C4×C8×C139C2211yescharacteristic
25C2×Dic278D411yescharacteristic
26C2×Dic278D411yescharacteristic
27C22×Dic139—22no—
28#14555775—42no—
29C2×C139⋊C8—21no—
30C2×C139⋊C8—21no—
31C4⋊Dic139D411yescharacteristic
32C4⋊Dic139D411yescharacteristic
33Dic139⋊C4—21no—
34Dic139⋊C4—21no—
35C22⋊Dic139—22no—
36C22⋊Dic139—22no—
37C22⋊Dic139—22no—
38C4×Dic139—21no—
39C4×Dic139—21no—
40C2×Q8×C139—21no—
41C2×D4×C139—21no—
42C2×D4×C139—21no—
43C2×D4×C139D412yes—
44C2×C8×C139—21no—
45C4⋊C4×C139—21no—
46C4⋊C4×C139—21no—
47C42×C139C2311yescharacteristic
48Dic278—21no—
49Dic278—21no—
50Dic278—21no—
51Dic278—21no—
52C2×Dic139—21no—
53C2×Dic139—21no—
54C2×Dic139—21no—
55C2×Dic139—21no—
56C2×Dic139—82no—
57C139⋊C8—41no—
58C139⋊C8—41no—
59C23×C139—22no—
60Q8×C139—41no—
61Q8×C139—41no—
62D4×C139—42no—
63D4×C139—41no—
64D4×C139—41no—
65D4×C139—41no—
66D4×C139—41no—
67C2×C4×C139—41no—
68C2×C4×C139C2×D411yescharacteristic
69C2×C4×C139C2×D411yescharacteristic
70C2×C4×C139C2×D411yescharacteristic
71C8×C139—41no—
72C22×C139—42no—
73C22×C139—42no—
74C22×C139—42no—
75C22×C139#12011yescharacteristic
76C4×C139—21no—
77C4×C139—81no—
78C4×C139#13511yescharacteristic
79C4×C139#13511yescharacteristic
80C4×C139AGL(1,ℤ/8)11yescharacteristic
81C4×C139#13711yescharacteristic
82Dic139—41no—
83Dic139—41no—
84Dic139—41no—
85Dic139—41no—
86C2×C139—82no—
87C2×C139#44911yescharacteristic
88C2×C139#45211yescharacteristic
89C2×C139#45511yescharacteristic
90C139#164011yescharacteristic, complemented, Sylow
91#1640—1391nomaximal, Sylow
92#559—1391no—
93#486D13911yescharacteristic
94#475—1391no—
95#462—1391no—
96#331—1391no—
97Q8⋊C8—1391no—
98Q8⋊C8—1391no—
99C2×Q16—2781no—
100C4⋊Q8C2×D13911yescharacteristic
101#127C2×D13911yescharacteristic
102#124—2781no—
103#124—2781no—
104#123—2782no—
105C4×Q8—1391no—
106C4×Q8—1391no—
107C4×D4—2781no—
108C4×D4—2781no—
109#106—2781no—
110C4⋊C8—1391no—
111C4⋊C8—1391no—
112#103—2781no—
113#103—2781no—
114#102—22no—
115C4×C8C2×D13911yescharacteristic
116C2×Q8—21no—
117C2×Q8—1391no—
118C2×Q8—1391no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D13912yes—
122C22×C4—2782no—
123Q16—5562no—
124C2×C8—21no—
125C2×C8—2781no—
126C2×C8—2781no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2781no—
130C4⋊C4—2781no—
131C4⋊C4—1391no—
132C4⋊C4—1391no—
133C22⋊C4—2782no—
134C22⋊C4—2782no—
135C22⋊C4—2782no—
136C42—2781no—
137C42—2781no—
138C42C22×D13911yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—2781no—
143Q8—2781no—
144Q8—2781no—
145Q8—2781no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—2781no—
153C2×C4—2781no—
154C2×C4—2781no—
155C2×C4—2781no—
156C2×C4—11122no—
157C2×C4D4×D13911yescharacteristic
158C2×C4D4×D13911yescharacteristic
159C2×C4C2×C22⋊D13911yescharacteristic
160C8—41no—
161C8—5561no—
162C8—5561no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1798481011yescharacteristic
167C4—21no—
168C4—81no—
169C4—5561no—
170C4—5561no—
171C4—5561no—
172C4—5561no—
173C4#1798486111yescharacteristic
174C4#1798486311yescharacteristic
175C4#1798486611yescharacteristic
176C4#1798487111yescharacteristic
177C2—82no—
178C2#2258109511yescharacteristic
179C2#2258111211yescharacteristic
180C2#2258113011yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#486×C139C2
socleC22×C139#120
prime radical#127×C139C22
hypercenter#486D139
hypocenterC139#1640
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #22581235C2semidirect
3. #22581160C2semidirect
5. #22580685C2semidirect
6. #22580685C2semidirect
90. C139#1640semidirect

Maximal subgroups

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

subgroupindex
#225816892
#225812352
#225811602
#225806972
#225806852
#486×C1392
#1640139