Finite Group Databasebeta

← #31805572

Subgroups — #31805572

Order 17792.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic278C211yesmaximal, characteristic
2#22581304C211yesmaximal, characteristic, complemented
3#22581249C211yesmaximal, characteristic, complemented
4#22581243C211yesmaximal, characteristic
5#22580700C211yesmaximal, characteristic, complemented
6#22580685C211yesmaximal, characteristic, complemented
7D4⋊C8×C139C211yesmaximal, characteristic
8C22×Dic278—21no—
9#17984842C2211yescharacteristic
10#17984842C2211yescharacteristic
11#17984841—21no—
12#17984821—21no—
13#17984819—22no—
14C4×Dic278C2211yescharacteristic
15D4×Dic139—21no—
16#17984776—21no—
17#17984773—21no—
18C4⋊(C139⋊C8)C2211yescharacteristic
19#17984767—21no—
20#17984767—22no—
21#17984763—21no—
22C4×D4×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4×C8×C139C2211yescharacteristic
25C2×Dic278—22no—
26C2×Dic278—21no—
27C2×Dic278—21no—
28C2×Dic278—42no—
29C2×Dic278—42no—
30C2×Dic278D411yescharacteristic
31C22×Dic139—22no—
32C2×C139⋊C8—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139D411yescharacteristic
37C4⋊Dic139D412yes—
38Dic139⋊C4—22no—
39Dic139⋊C4—21no—
40C22⋊Dic139—22no—
41C4×Dic139—21no—
42C2×D4×C139D411yescharacteristic
43C22×C4×C139—21no—
44C2×C8×C139—21no—
45C2×C8×C139—21no—
46C4⋊C4×C139D411yescharacteristic
47C22⋊C4×C139—21no—
48C42×C139C2311yescharacteristic
49Dic278—21no—
50Dic278—44no—
51Dic278—41no—
52Dic278—41no—
53Dic278—42no—
54Dic278SD1612yes—
55C2×Dic139—21no—
56C2×Dic139—21no—
57C2×Dic139—22no—
58C2×Dic139—44no—
59C2×Dic139—41no—
60C139⋊C8—41no—
61C23×C139—21no—
62D4×C139—21no—
63D4×C139Q1612yes—
64C2×C4×C139—21no—
65C2×C4×C139—41no—
66C2×C4×C139—41no—
67C2×C4×C139C2×D411yescharacteristic
68C2×C4×C139C2×D411yescharacteristic
69C2×C4×C139C2×D411yescharacteristic
70C8×C139—41no—
71C8×C139—41no—
72C22×C139—22no—
73C22×C139—41no—
74C22×C139—41no—
75C22×C139#12011yescharacteristic
76C4×C139—21no—
77C4×C139—41no—
78C4×C139C2×SD1611yescharacteristic
79C4×C139C2×Q1611yescharacteristic
80C4×C139AGL(1,ℤ/8)11yescharacteristic
81C4×C139#13711yescharacteristic
82Dic139—22no—
83Dic139—42no—
84Dic139—41no—
85Dic139—81no—
86C2×C139—42no—
87C2×C139#45011yescharacteristic
88C2×C139#45111yescharacteristic
89C2×C139#45411yescharacteristic
90C139#163711yescharacteristic, complemented, Sylow
91#1637—1391nomaximal, Sylow
92D4×Q8—1391no—
93#487—1391no—
94#477—1391no—
95#476—1391no—
96#332—1391no—
97Q8⋊C8—1391no—
98D4⋊C8D13911yescharacteristic
99C22×Q8—2781no—
100C4⋊Q8—2781no—
101C4⋊Q8—1391no—
102C4⋊Q8—1391no—
103C22⋊Q8—2782no—
104C22⋊Q8—2781no—
105C4×Q8—1391no—
106C4×D4—2781no—
107C4×D4C2×D13911yescharacteristic
108#107—2781no—
109#106—2781no—
110C4⋊C8—1391no—
111C4⋊C8C2×D13911yescharacteristic
112#103—2781no—
113#103—2782no—
114#102—2781no—
115C4×C8C2×D13911yescharacteristic
116C2×Q8—2782no—
117C2×Q8—2781no—
118C2×Q8—2781no—
119C2×Q8—5562no—
120C2×Q8—5562no—
121C2×Q8—1391no—
122C2×D4D55611yescharacteristic
123C22×C4—21no—
124C22×C4—2782no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—2781no—
128C4⋊C4—2782no—
129C4⋊C4—2781no—
130C4⋊C4—2781no—
131C4⋊C4—2781no—
132C4⋊C4—2781no—
133C4⋊C4—1392no—
134C4⋊C4—1391no—
135C4⋊C4D55611yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—2782no—
138C42—2781no—
139C42C22×D13911yescharacteristic
140C23—21no—
141Q8—2781no—
142Q8—5562no—
143Q8—5564no—
144Q8—5561no—
145Q8—5561no—
146Q8—1392no—
147D4—21no—
148D4Dic55612yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—2781no—
153C2×C4—2781no—
154C2×C4—2782no—
155C2×C4—5564no—
156C2×C4—5561no—
157C2×C4D4×D13911yescharacteristic
158C2×C4D4×D13911yescharacteristic
159C2×C4C2×D55611yescharacteristic
160C8—41no—
161C8—41no—
162C8—5561no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1798481211yescharacteristic
167C4—21no—
168C4—41no—
169C4—2782no—
170C4—5562no—
171C4—5561no—
172C4—11121no—
173C4SD16×D13911yescharacteristic
174C4C2×Dic55611yescharacteristic
175C4#1798486611yescharacteristic
176C4#1798487511yescharacteristic
177C2—42no—
178C2#2258110511yescharacteristic
179C2#2258111111yescharacteristic
180C2#2258112711yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
FittingD4⋊C8×C139C2
socleC22×C139#120
prime radicalC2×D4×C139D4
hypercenterD4⋊C8D139
hypocenterC139#1637
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. #22581304C2semidirect
3. #22581249C2semidirect
5. #22580700C2semidirect
6. #22580685C2semidirect
90. C139#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2782
#225813042
#225812492
#225812432
#225807002
#225806852
D4⋊C8×C1392
#1637139