Finite Group Databasebeta

← #31805672

Subgroups — #31805672

Order 17792.

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

normal subgroups only

This group has 200 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#22581676C211yesmaximal, characteristic
2#22581349C211yesmaximal, characteristic, complemented
3#22581230C211yesmaximal, characteristic
4#22580698C211yesmaximal, characteristic, complemented
5Q8⋊(C139⋊C8)C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic
7#462×C139C211yesmaximal, characteristic, complemented
8#17984842C2211yescharacteristic
9#17984837—22no—
10#17984830—21no—
11#17984818—21no—
12C4×Dic278—21no—
13C4×D556C2211yescharacteristic
14#17984800—21no—
15#17984775—21no—
16#17984773—22no—
17C4⋊(C139⋊C8)C2211yescharacteristic
18#17984762—21no—
19C4×C139⋊C8C2211yescharacteristic
20C2×Q16×C139—21no—
21C4⋊Q8×C139C2211yescharacteristic
22C4×Q8×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24#103×C139—21no—
25C2×Dic278—21no—
26C2×D556D411yescharacteristic
27C2×C4×D139—21no—
28C2×C139⋊C8—21no—
29C2×C139⋊C8—21no—
30C4⋊Dic139—21no—
31C4⋊Dic139D412yes—
32C4⋊Dic139D411yescharacteristic
33Dic139⋊C4—22no—
34(C2×D139)⋊C4—22no—
35(C2×D139)⋊C4—22no—
36(C2×D139)⋊C4—21no—
37C4×Dic139—22no—
38C2×Q8×C139—21no—
39C2×Q8×C139D411yescharacteristic
40Q16×C139—42no—
41C2×C8×C139—21no—
42C4⋊C4×C139—21no—
43C4⋊C4×C139—21no—
44C4⋊C4×C139—21no—
45C4⋊C4×C139D411yescharacteristic
46C42×C139—21no—
47C42×C139C2311yescharacteristic
48C22×D139—21no—
49Dic278—41no—
50Dic278—41no—
51D556—21no—
52D556—21no—
53C2×Dic139—21no—
54C2×Dic139—22no—
55C4×D139—41no—
56C4×D139—41no—
57C139⋊C8—22no—
58C139⋊C8—41no—
59Q8×C139—21no—
60Q8×C139—21no—
61Q8×C139—41no—
62Q8×C139—41no—
63C2×C4×C139—21no—
64C2×C4×C139—21no—
65C2×C4×C139—41no—
66C2×C4×C139C2×D411yescharacteristic
67C2×C4×C139C2×D411yescharacteristic
68C2×C4×C139C2×D411yescharacteristic
69C8×C139—41no—
70C22×C139#12011yescharacteristic
71C2×D139—41no—
72C2×D139—41no—
73C2×D139—41no—
74C4×C139—21no—
75C4×C139—41no—
76C4×C139—41no—
77C4×C139—81no—
78C4×C139#13511yescharacteristic
79C4×C139#13511yescharacteristic
80C4×C139AGL(1,ℤ/8)11yescharacteristic
81C4×C139#13711yescharacteristic
82Dic139—41no—
83Dic139—42no—
84C2×C139#44911yescharacteristic
85C2×C139#45211yescharacteristic
86C2×C139#45611yescharacteristic
87D139—81no—
88C139#165211yescharacteristic, complemented, Sylow
89#1652—1391nomaximal, Sylow
90#556—1391no—
91#498—1391no—
92#474—1391no—
93#462D13911yescharacteristic, complemented
94#332—1391no—
95Q8⋊C8—1391no—
96D4⋊C8—1391no—
97C2×Q16—21no—
98C4⋊Q8—1391no—
99C4⋊Q8C2×D13911yescharacteristic
100#126—2782no—
101#124—2781no—
102C22⋊Q8—2781no—
103C4×Q8—2781no—
104C4×Q8C2×D13911yescharacteristic
105C4×D4—1391no—
106#117—2781no—
107#107—2781no—
108#106—2782no—
109C4⋊C8—1391no—
110C4⋊C8C2×D13911yescharacteristic
111#103—21no—
112#102—2781no—
113C4×C8—1391no—
114C2×Q8—21no—
115C2×Q8—2781no—
116C2×Q8C22⋊D13911yescharacteristic
117C2×D4—1391no—
118C22×C4—2781no—
119Q16—42no—
120C2×C8—21no—
121C2×C8—2781no—
122C2×C8—2781no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2782no—
127C4⋊C4—2781no—
128C4⋊C4—1392no—
129C4⋊C4—1391no—
130C4⋊C4C22⋊D13911yescharacteristic
131C22⋊C4—2782no—
132C22⋊C4—2782no—
133C22⋊C4—2781no—
134C42—21no—
135C42—2782no—
136C42C22×D13911yescharacteristic
137C23—2781no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—5561no—
143Q8—5561no—
144D4—2781no—
145D4—2781no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—2781no—
150C2×C4—2782no—
151C2×C4—5561no—
152C2×C4—5561no—
153C2×C4D4×D13911yescharacteristic
154C2×C4D4×D13911yescharacteristic
155C2×C4C2×C22⋊D13911yescharacteristic
156C8—41no—
157C8—2782no—
158C8—5561no—
159C22—5561no—
160C22—5561no—
161C22—5561no—
162C22#1798481011yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—5561no—
168C4—5562no—
169C4#1798486211yescharacteristic
170C4#1798486511yescharacteristic
171C4#1798486811yescharacteristic
172C4#1798487411yescharacteristic
173C2—11121no—
174C2#2258109611yescharacteristic
175C2#2258111411yescharacteristic
176C2#2258113411yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#462×C139C2
socleC22×C139#120
prime radicalC2×D556D4
hypercenter#462D139
hypocenterC139#1652
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #22581349C2semidirect
4. #22580698C2semidirect
5. Q8⋊(C139⋊C8)C2semidirect
7. #462×C139C2semidirect
88. C139#1652semidirect
93. #462D139semidirect

Maximal subgroups

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

subgroupindex
#225816762
#225813492
#225812302
#225806982
Q8⋊(C139⋊C8)2
#225806802
#462×C1392
#1652139