Finite Group Databasebeta

← #31805528

Subgroups — #31805528

Order 17792.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#22581623C211yesmaximal, characteristic
2#22581245C211yesmaximal, characteristic, complemented
3#22581240C211yesmaximal, characteristic, complemented
4#22580697C211yesmaximal, characteristic, complemented
5#22580685C211yesmaximal, characteristic, complemented
6#22580682C211yesmaximal, characteristic, complemented
7#492×C139C211yesmaximal, characteristic, complemented
8C2×#14555784—21no—
9#17984838—21no—
10#17984814—22no—
11#17984813—21no—
12C4×Dic278C2211yescharacteristic
13C4×D556C2211yescharacteristic
14D4×Dic139—21no—
15#17984775—21no—
16#17984773—21no—
17C4⋊(C139⋊C8)C2211yescharacteristic
18C4⋊(C139⋊C8)C2211yescharacteristic
19#17984765—21no—
20#17984762—21no—
21C2×SD16×C139—22no—
22C4⋊Q8×C139C2211yescharacteristic
23#127×C139C2211yescharacteristic
24C4×C8×C139C2211yescharacteristic
25#14555784—42no—
26#14555784—42no—
27C2×Dic278D411yescharacteristic
28C2×D556D411yescharacteristic
29C2×C22⋊D139—22no—
30C2×C22⋊D139—22no—
31C22×Dic139—22no—
32C2×C4×D139—21no—
33C2×C139⋊C8—21no—
34C2×C139⋊C8—21no—
35C4⋊Dic139D411yescharacteristic
36C4⋊Dic139D411yescharacteristic
37Dic139⋊C4—21no—
38C22⋊Dic139—22no—
39(C2×D139)⋊C4—21no—
40C4×Dic139—21no—
41C2×Q8×C139—21no—
42C2×D4×C139—21no—
43C2×D4×C139—21no—
44C2×D4×C139D412yes—
45SD16×C139—44no—
46C2×C8×C139—21no—
47C4⋊C4×C139—21no—
48C4⋊C4×C139—21no—
49C42×C139C2311yescharacteristic
50C22×D139—21no—
51Dic278—21no—
52Dic278SD1612yescomplemented
53D556—21no—
54D556—21no—
55C22⋊D139—44no—
56C22⋊D139—82no—
57C2×Dic139—21no—
58C2×Dic139—21no—
59C2×Dic139—21no—
60C2×Dic139—44no—
61C4×D139—41no—
62C4×D139—41no—
63C139⋊C8—41no—
64C139⋊C8—41no—
65C23×C139—22no—
66Q8×C139—42no—
67D4×C139—42no—
68D4×C139—41no—
69D4×C139—41no—
70D4×C139—41no—
71D4×C139—41no—
72C2×C4×C139—41no—
73C2×C4×C139C2×D411yescharacteristic
74C2×C4×C139C2×D411yescharacteristic
75C2×C4×C139C2×D411yescharacteristic
76C8×C139—22no—
77C22×C139—42no—
78C22×C139—42no—
79C22×C139—42no—
80C22×C139#12011yescharacteristic
81C2×D139—41no—
82C2×D139—41no—
83C2×D139—41no—
84C4×C139—21no—
85C4×C139—81no—
86C4×C139C2×SD1611yescharacteristic
87C4×C139#13511yescharacteristic
88C4×C139AGL(1,ℤ/8)11yescharacteristic
89C4×C139#13711yescharacteristic
90Dic139—22no—
91Dic139—41no—
92Dic139—41no—
93C2×C139—82no—
94C2×C139#45011yescharacteristic
95C2×C139#45211yescharacteristic
96C2×C139#45311yescharacteristic
97D139—81no—
98C139#163111yescharacteristic, complemented, Sylow
99#1631—1391nomaximal, Sylow
100#550—1391no—
101#492D13911yescharacteristic, complemented
102#477—1391no—
103#476—1391no—
104#331—1391no—
105Q8⋊C8—1391no—
106D4⋊C8—1391no—
107C2×#41—2781no—
108C2×SD16—22no—
109C4⋊Q8C2×D13911yescharacteristic
110#127—2781no—
111#127C2×D13911yescharacteristic
112#121—2782no—
113#121—2781no—
114C4×Q8—1391no—
115C4×D4—2781no—
116C4×D4—1391no—
117#107—2781no—
118#106—2781no—
119C4⋊C8—1391no—
120C4⋊C8—1391no—
121#103—2781no—
122#102—2781no—
123C4×C8C2×D13911yescharacteristic
124#41—5562no—
125#41—5562no—
126C2×Q8—21no—
127C2×Q8—1391no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—2782no—
131C2×D4—2782no—
132C2×D4—1391no—
133C2×D4C22⋊D13912yes—
134C22×C4—2782no—
135C22×C4—2781no—
136SD16—44no—
137C2×C8—21no—
138C2×C8—2781no—
139C2×C8—2781no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—2781no—
143C4⋊C4—1391no—
144C4⋊C4—1391no—
145C22⋊C4—2782no—
146C22⋊C4—2781no—
147C42—2781no—
148C42C22×D13911yescharacteristic
149C23—22no—
150C23—2781no—
151Q8—42no—
152Q8—2781no—
153Q8—1392no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—2781no—
160D4—2781no—
161D4—5564no—
162D4—11122no—
163C2×C4—41no—
164C2×C4—2781no—
165C2×C4—2781no—
166C2×C4—2781no—
167C2×C4—5564no—
168C2×C4—5561no—
169C2×C4—5561no—
170C2×C4D4×D13911yescharacteristic
171C2×C4D4×D13911yescharacteristic
172C2×C4C2×C22⋊D13911yescharacteristic
173C8—22no—
174C8—5561no—
175C8—5561no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—5561no—
180C22—5561no—
181C22—5561no—
182C22#1798481011yescharacteristic
183C4—21no—
184C4—81no—
185C4—2782no—
186C4—5561no—
187C4—5561no—
188C4SD16×D13911yescharacteristic
189C4#1798486311yescharacteristic
190C4#1798486911yescharacteristic
191C4#1798487111yescharacteristic
192C2—82no—
193C2—11121no—
194C2#2258110211yescharacteristic
195C2#2258111211yescharacteristic
196C2#2258112011yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#492×C139C2
socleC22×C139#120
prime radical#22581623C2
hypercenter#492D139
hypocenterC139#1631
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #22581245C2semidirect
3. #22581240C2semidirect
4. #22580697C2semidirect
5. #22580685C2semidirect
6. #22580682C2semidirect
7. #492×C139C2semidirect
52. Dic278SD16semidirect
98. C139#1631semidirect
101. #492D139semidirect

Maximal subgroups

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

subgroupindex
#225816232
#225812452
#225812402
#225806972
#225806852
#225806822
#492×C1392
#1631139