Finite Group Databasebeta

← #31805540

Subgroups — #31805540

Order 17792.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#22581660C211yesmaximal, characteristic
2#22581333C211yesmaximal, characteristic, complemented
3#22581249C211yesmaximal, characteristic, complemented
4#22581243C211yesmaximal, characteristic
5#22580701C211yesmaximal, characteristic, complemented
6#22580685C211yesmaximal, characteristic, complemented
7D4⋊C8×C139C211yesmaximal, characteristic
8C2×Dic556—22no—
9#17984842C2211yescharacteristic
10#17984842C2211yescharacteristic
11#17984833—21no—
12#17984821—21no—
13#17984819—22no—
14C4×Dic278C2211yescharacteristic
15D4×Dic139—21no—
16C2×C4⋊Dic139—21no—
17#17984776—21no—
18#17984773—21no—
19C4⋊(C139⋊C8)C2211yescharacteristic
20#17984767—21no—
21#17984763—21no—
22C4×D4×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4×C8×C139C2211yescharacteristic
25C2×Dic278—21no—
26C2×Dic278D411yescharacteristic
27C2×Dic278D412yes—
28C22×Dic139—22no—
29Dic556—44no—
30C2×C139⋊C8—21no—
31C4⋊Dic139—22no—
32C4⋊Dic139—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139D411yescharacteristic
37Dic139⋊C4—22no—
38Dic139⋊C4—21no—
39C22⋊Dic139—22no—
40C4×Dic139—21no—
41C2×D4×C139D411yescharacteristic
42C22×C4×C139—21no—
43C2×C8×C139—21no—
44C2×C8×C139—21no—
45C4⋊C4×C139D411yescharacteristic
46C22⋊C4×C139—21no—
47C42×C139C2311yescharacteristic
48Dic278—21no—
49Dic278—21no—
50Dic278—42no—
51Dic278—42no—
52C2×Dic139—21no—
53C2×Dic139—21no—
54C2×Dic139—22no—
55C2×Dic139—41no—
56C2×Dic139—82no—
57C139⋊C8—41no—
58C23×C139—21no—
59D4×C139—21no—
60D4×C139Q1612yescomplemented
61C2×C4×C139—21no—
62C2×C4×C139—41no—
63C2×C4×C139—41no—
64C2×C4×C139C2×D411yescharacteristic
65C2×C4×C139C2×D411yescharacteristic
66C2×C4×C139C2×D411yescharacteristic
67C8×C139—22no—
68C8×C139—41no—
69C22×C139—22no—
70C22×C139—41no—
71C22×C139—41no—
72C22×C139#12011yescharacteristic
73C4×C139—21no—
74C4×C139—41no—
75C4×C139C2×Q1611yescharacteristic
76C4×C139#13511yescharacteristic
77C4×C139#13711yescharacteristic
78C4×C139#13711yescharacteristic
79Dic139—41no—
80Dic139—41no—
81Dic139—42no—
82Dic139—81no—
83C2×C139—42no—
84C2×C139#45111yescharacteristic
85C2×C139#45211yescharacteristic
86C2×C139#45311yescharacteristic
87C139#163211yescharacteristic, complemented, Sylow
88#1632—1391nomaximal, Sylow
89#554—1391no—
90#494—1391no—
91#477—1391no—
92#476—1391no—
93#333—1391no—
94Q8⋊C8—1391no—
95D4⋊C8D13911yescharacteristic
96C2×Q16—2782no—
97C4⋊Q8—1391no—
98C4⋊Q8—1391no—
99#125—2781no—
100C22⋊Q8—2782no—
101C22⋊Q8—2781no—
102C4×Q8—1391no—
103C4×D4—2781no—
104C4×D4C2×D13911yescharacteristic
105C2×C4⋊C4—2781no—
106#107—2781no—
107#106—2781no—
108C4⋊C8—1391no—
109C4⋊C8C2×D13911yescharacteristic
110#103—2781no—
111#102—2781no—
112C4×C8C2×D13911yescharacteristic
113C2×Q8—2781no—
114C2×Q8—1391no—
115C2×Q8—1392no—
116C2×D4D55611yescharacteristic
117C22×C4—21no—
118C22×C4—2782no—
119Q16—5564no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2781no—
123C4⋊C4—2782no—
124C4⋊C4—2782no—
125C4⋊C4—2781no—
126C4⋊C4—2781no—
127C4⋊C4—2781no—
128C4⋊C4—2781no—
129C4⋊C4—2781no—
130C4⋊C4—1391no—
131C4⋊C4D55611yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—2782no—
134C42—2781no—
135C42C22×D13911yescharacteristic
136C23—21no—
137Q8—2781no—
138Q8—2781no—
139Q8—5562no—
140Q8—5562no—
141D4—21no—
142D4Dic55612yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—2781no—
147C2×C4—2781no—
148C2×C4—2782no—
149C2×C4—5561no—
150C2×C4—11122no—
151C2×C4D4×D13911yescharacteristic
152C2×C4D4×D13911yescharacteristic
153C2×C4C2×D55611yescharacteristic
154C8—22no—
155C8—41no—
156C8—5561no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1798481211yescharacteristic
161C4—21no—
162C4—41no—
163C4—5561no—
164C4—5561no—
165C4—5562no—
166C4—11121no—
167C4C2×Dic55611yescharacteristic
168C4#1798486111yescharacteristic
169C4#1798487111yescharacteristic
170C4#1798487511yescharacteristic
171C2—42no—
172C2#2258111111yescharacteristic
173C2#2258111611yescharacteristic
174C2#2258112211yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
FittingD4⋊C8×C139C2
socleC22×C139#120
prime radicalC2×D4×C139D4
hypercenterD4⋊C8D139
hypocenterC139#1632
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #22581333C2semidirect
3. #22581249C2semidirect
5. #22580701C2semidirect
6. #22580685C2semidirect
60. D4×C139Q16semidirect
87. C139#1632semidirect
142. D4Dic556semidirect

Maximal subgroups

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

subgroupindex
#225816602
#225813332
#225812492
#225812432
#225807012
#225806852
D4⋊C8×C1392
#1632139