Finite Group Databasebeta

← #31805741

Subgroups — #31805741

Order 17792.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#22581703C211yesmaximal, characteristic
2#22581362C211yesmaximal, characteristic, complemented
3#22581322C211yesmaximal, characteristic, complemented
4#22581312C211yesmaximal, characteristic
5#22580694C211yesmaximal, characteristic, complemented
6#22580694C211yesmaximal, characteristic, complemented
7#329×C139C211yesmaximal, characteristic
8#17984842C2211yescharacteristic
9#17984840—21no—
10#17984835—21no—
11#17984835—21no—
12#17984834C2211yescharacteristic
13#17984834C2211yescharacteristic
14#17984823—21no—
15#17984819—21no—
16#17984819—21no—
17#17984776—21no—
18#17984774—21no—
19#17984767—21no—
20#17984767—21no—
21#17984766—21no—
22#17984763—21no—
23#17984753C2211yescharacteristic
24#124×C139C2211yescharacteristic
25#97×C139C2211yescharacteristic
26#97×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278—21no—
29C22×Dic139—21no—
30C2×C139⋊C8—21no—
31C4⋊Dic139—21no—
32C4⋊Dic139—21no—
33C4⋊Dic139D411yescharacteristic
34C4⋊Dic139D411yescharacteristic
35C4⋊Dic139D411yescharacteristic
36C4⋊Dic139D411yescharacteristic
37Dic139⋊C4—21no—
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40Dic139⋊C4—21no—
41Dic139⋊C4—21no—
42Dic139⋊C4—21no—
43C22⋊Dic139—21no—
44C22⋊Dic139—21no—
45C22⋊Dic139—21no—
46C4×Dic139—21no—
47C2×Q8×C139D411yescharacteristic
48C2×D4×C139D411yescharacteristic
49C2×C8×C139—21no—
50C2×C8×C139—21no—
51C22⋊C4×C139—21no—
52C22⋊C4×C139—21no—
53C42×C139C2311yescharacteristic
54Dic278—42no—
55Dic278—81no—
56C2×Dic139—21no—
57C2×Dic139—21no—
58C2×Dic139—21no—
59C2×Dic139—21no—
60C2×Dic139—41no—
61C2×Dic139—81no—
62C139⋊C8—41no—
63C23×C139—21no—
64Q8×C139—41no—
65D4×C139—41no—
66C2×C4×C139—21no—
67C2×C4×C139C2×D411yescharacteristic
68C2×C4×C139C2×D411yescharacteristic
69C2×C4×C139C2×D411yescharacteristic
70C8×C139—22no—
71C8×C139—41no—
72C22×C139—41no—
73C22×C139—41no—
74C22×C139—41no—
75C22×C139#12011yescharacteristic
76C4×C139—21no—
77C4×C139—21no—
78C4×C139—21no—
79C4×C139—41no—
80Dic139—41no—
81Dic139—41no—
82Dic139—41no—
83Dic139—41no—
84Dic139—81no—
85C2×C139—81no—
86C2×C139#45411yescharacteristic
87C2×C139#45511yescharacteristic
88C2×C139#45611yescharacteristic
89C139#166411yescharacteristic, complemented, Sylow
90#1664—1391nomaximal, Sylow
91#563—1391no—
92#501—1391no—
93#491—1391no—
94#489—1391no—
95#330—1391no—
96#330—1391no—
97#329D13911yescharacteristic
98C4⋊Q8—2781no—
99C4⋊Q8—1391no—
100#126—2781no—
101#126—2781no—
102#125—1391no—
103#125—1391no—
104#124C2×D13911yescharacteristic
105#123—2781no—
106C22⋊Q8—2781no—
107C22⋊Q8—2781no—
108#107—2781no—
109#106—2781no—
110#103—2781no—
111#103—2781no—
112#103—2781no—
113#102—2781no—
114#97—1391no—
115#97C2×D13911yescharacteristic
116#97C2×D13911yescharacteristic
117C2×Q8—2781no—
118C2×Q8—2781no—
119C2×Q8D55611yescharacteristic
120C2×D4D55611yescharacteristic
121C22×C4—2781no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—2781no—
125C4⋊C4—2781no—
126C4⋊C4—2781no—
127C4⋊C4—2781no—
128C4⋊C4—2781no—
129C4⋊C4—2781no—
130C4⋊C4—2781no—
131C4⋊C4—2781no—
132C4⋊C4—2781no—
133C4⋊C4—1391no—
134C4⋊C4—1391no—
135C4⋊C4—1391no—
136C4⋊C4—1391no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—2781no—
140C22⋊C4—2781no—
141C22⋊C4—2781no—
142C42—2781no—
143C42C22×D13911yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—5562no—
147Q8—11121no—
148D4—41no—
149C2×C4—21no—
150C2×C4—2781no—
151C2×C4—2781no—
152C2×C4—2781no—
153C2×C4—2781no—
154C2×C4—5561no—
155C2×C4—11121no—
156C2×C4D4×D13911yescharacteristic
157C2×C4D4×D13911yescharacteristic
158C2×C4C2×D55611yescharacteristic
159C8—22no—
160C8—41no—
161C8—5561no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1798481211yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—5561no—
171C4—5561no—
172C4—5561no—
173C4—5561no—
174C4—11121no—
175C2—81no—
176C2#2258112711yescharacteristic
177C2#2258113311yescharacteristic
178C2#2258113711yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#329×C139C2
socleC22×C139#120
prime radicalC2×D4×C139D4
hypercenter#329D139
hypocenterC139#1664
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #22581362C2semidirect
3. #22581322C2semidirect
5. #22580694C2semidirect
6. #22580694C2semidirect
89. C139#1664semidirect

Maximal subgroups

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

subgroupindex
#225817032
#225813622
#225813222
#225813122
#225806942
#329×C1392
#1664139