Finite Group Databasebeta

← #31805511

Subgroups — #31805511

Order 17792.

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

normal subgroups only

This group has 216 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#22581677C211yesmaximal, characteristic, complemented
2#22581150C211yesmaximal, characteristic, complemented
3#22581145C211yesmaximal, characteristic
4#22580699C211yesmaximal, characteristic, complemented
5#22580685C211yesmaximal, characteristic, complemented
6#22580682C211yesmaximal, characteristic, complemented
7#486×C139C211yesmaximal, characteristic, complemented
8C2×#14555773—21no—
9C2×#14555770—21no—
10#17984837—22no—
11#17984831—21no—
12#17984822—21no—
13Q8×Dic139—21no—
14C4×Dic278C2211yescharacteristic
15C4×D556C2211yescharacteristic
16#17984800—21no—
17C4⋊(C139⋊C8)C2211yescharacteristic
18C4⋊(C139⋊C8)C2211yescharacteristic
19#17984763—21no—
20#17984763—21no—
21C4⋊Q8×C139C2211yescharacteristic
22#127×C139C2211yescharacteristic
23#102×C139—22no—
24C4×C8×C139C2211yescharacteristic
25C2×Dic278D411yescharacteristic
26C2×D556D411yescharacteristic
27C2×C4×D139—21no—
28#14555773—42no—
29#14555770—42no—
30C2×C139⋊C8—21no—
31C2×C139⋊C8—21no—
32C4⋊Dic139—22no—
33C4⋊Dic139D411yescharacteristic
34C4⋊Dic139D411yescharacteristic
35Dic139⋊C4—21no—
36(C2×D139)⋊C4—22no—
37(C2×D139)⋊C4—22no—
38(C2×D139)⋊C4—21no—
39C4×Dic139—22no—
40C4×Dic139—21no—
41C2×Q8×C139—21no—
42C2×D4×C139—21no—
43C2×D4×C139—21no—
44C2×D4×C139—21no—
45C2×C8×C139—21no—
46C4⋊C4×C139—21no—
47C4⋊C4×C139D412yes—
48C42×C139C2311yescharacteristic
49C22×D139—21no—
50Dic278—21no—
51Dic278—21no—
52D556—21no—
53D556—21no—
54C2×Dic139—21no—
55C2×Dic139—21no—
56C2×Dic139—21no—
57C4×D139—41no—
58C4×D139—41no—
59C139⋊C8—41no—
60C139⋊C8—41no—
61C23×C139—41no—
62Q8×C139—41no—
63Q8×C139—41no—
64D4×C139—42no—
65D4×C139—41no—
66D4×C139—41no—
67D4×C139—41no—
68D4×C139—41no—
69C2×C4×C139—22no—
70C2×C4×C139C2×D411yescharacteristic
71C2×C4×C139C2×D411yescharacteristic
72C2×C4×C139C2×D411yescharacteristic
73C8×C139—41no—
74C22×C139—81no—
75C22×C139—81no—
76C22×C139—81no—
77C22×C139#12011yescharacteristic
78C2×D139—41no—
79C2×D139—41no—
80C2×D139—41no—
81C4×C139—21no—
82C4×C139—42no—
83C4×C139#13511yescharacteristic
84C4×C139#13511yescharacteristic
85C4×C139AGL(1,ℤ/8)11yescharacteristic
86C4×C139AGL(1,ℤ/8)11yescharacteristic
87Dic139—41no—
88Dic139—41no—
89Dic139—41no—
90C2×C139—161no—
91C2×C139#44911yescharacteristic
92C2×C139#44911yescharacteristic
93C2×C139#45411yescharacteristic
94D139—81no—
95C139#162811yescharacteristic, complemented, Sylow
96#1628—1391nomaximal, Sylow
97#556—1391no—
98#486D13911yescharacteristic, complemented
99#460—1391no—
100#459—1391no—
101#332—1391no—
102Q8⋊C8—1391no—
103D4⋊C8—1391no—
104C2×SD16—2781no—
105C2×D8—2781no—
106C4⋊Q8C2×D13911yescharacteristic
107#127C2×D13911yescharacteristic
108#126—2782no—
109#124—2781no—
110C22⋊Q8—2781no—
111C4×Q8—2781no—
112C4×Q8—1391no—
113C4×D4—1391no—
114#117—2781no—
115C4⋊C8—1391no—
116C4⋊C8—1391no—
117#102—22no—
118#102—2781no—
119#102—2781no—
120C4×C8C2×D13911yescharacteristic
121C2×Q8—21no—
122C2×Q8—1391no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—1391no—
127C22×C4—2781no—
128SD16—5562no—
129D8—5562no—
130C2×C8—21no—
131C2×C8—2781no—
132C2×C8—2781no—
133C4⋊C4—21no—
134C4⋊C4—2782no—
135C4⋊C4—2781no—
136C4⋊C4—1391no—
137C4⋊C4—1391no—
138C4⋊C4C22⋊D13912yes—
139C22⋊C4—2782no—
140C22⋊C4—2782no—
141C22⋊C4—2781no—
142C42—2782no—
143C42—2781no—
144C42C22×D13911yescharacteristic
145C23—41no—
146C23—2781no—
147Q8—41no—
148Q8—41no—
149Q8—2781no—
150Q8—2781no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—2781no—
157D4—2781no—
158C2×C4—22no—
159C2×C4—2781no—
160C2×C4—2781no—
161C2×C4—2781no—
162C2×C4—5561no—
163C2×C4—5561no—
164C2×C4D4×D13911yescharacteristic
165C2×C4D4×D13911yescharacteristic
166C2×C4C2×C22⋊D13911yescharacteristic
167C8—41no—
168C8—5561no—
169C8—5561no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—5561no—
174C22—5561no—
175C22—5561no—
176C22#1798481011yescharacteristic
177C4—21no—
178C4—42no—
179C4—5561no—
180C4—5561no—
181C4—5561no—
182C4#1798486111yescharacteristic
183C4#1798486311yescharacteristic
184C4#1798486611yescharacteristic
185C4#1798486911yescharacteristic
186C2—161no—
187C2—11121no—
188C2#2258109511yescharacteristic
189C2#2258109711yescharacteristic
190C2#2258112511yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#486×C139C2
socleC22×C139#120
prime radical#22581145C2
hypercenter#486D139
hypocenterC139#1628
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #22581677C2semidirect
2. #22581150C2semidirect
4. #22580699C2semidirect
5. #22580685C2semidirect
6. #22580682C2semidirect
7. #486×C139C2semidirect
95. C139#1628semidirect
98. #486D139semidirect

Maximal subgroups

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

subgroupindex
#225816772
#225811502
#225811452
#225806992
#225806852
#225806822
#486×C1392
#1628139