Finite Group Databasebeta

← #31805605

Subgroups — #31805605

Order 17792.

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

normal subgroups only

This group has 250 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#22581299C211yesmaximal, characteristic, complemented
3#22581239C211yesmaximal, characteristic, complemented
4#22581159C211yesmaximal, characteristic, complemented
5#22580683C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic, complemented
7#331×C139C211yesmaximal, characteristic, complemented
8C2×#14555784—21no—
9C2×#14555774—21no—
10#17984842C2211yescharacteristic
11#17984838—21no—
12#17984814—22no—
13#17984813—21no—
14C4×Dic278C2211yescharacteristic
15C4×D556C2211yescharacteristic
16D4×Dic139—21no—
17#17984774—21no—
18#17984767—21no—
19#17984767—21no—
20#17984763—22no—
21C4×C139⋊C8C2211yescharacteristic
22#127×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4⋊C8×C139C2211yescharacteristic
25#14555784—42no—
26#14555784—42no—
27C2×Dic278—21no—
28C2×Dic278D411yescharacteristic
29C2×D556D411yescharacteristic
30C2×C22⋊D139—22no—
31C2×C22⋊D139—22no—
32C22×Dic139—22no—
33C2×C4×D139—21no—
34#14555774—42no—
35C2×C139⋊C8—21no—
36C4⋊Dic139—21no—
37C4⋊Dic139—21no—
38C4⋊Dic139D411yescharacteristic
39C4⋊Dic139D411yescharacteristic
40Dic139⋊C4—21no—
41C22⋊Dic139—22no—
42(C2×D139)⋊C4—21no—
43C4×Dic139—21no—
44C2×D4×C139—21no—
45C2×D4×C139—21no—
46C2×D4×C139D412yes—
47C2×C8×C139—21no—
48C2×C8×C139—21no—
49C42×C139C2311yescharacteristic
50C22×D139—21no—
51Dic278—21no—
52Dic278—41no—
53Dic278—41no—
54Dic278SD1612yescomplemented
55D556—21no—
56D556—21no—
57C22⋊D139—44no—
58C22⋊D139—82no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C2×Dic139—44no—
63C2×Dic139—41no—
64C4×D139—41no—
65C4×D139—41no—
66C139⋊C8—41no—
67C23×C139—22no—
68D4×C139—42no—
69D4×C139—41no—
70D4×C139—41no—
71D4×C139—41no—
72D4×C139—41no—
73C2×C4×C139C2×D411yescharacteristic
74C2×C4×C139C2×D411yescharacteristic
75C2×C4×C139C2×D411yescharacteristic
76C8×C139—41no—
77C8×C139—41no—
78C22×C139—42no—
79C22×C139—42no—
80C22×C139—42no—
81C22×C139#12011yescharacteristic
82C2×D139—41no—
83C2×D139—41no—
84C2×D139—41no—
85C4×C139—21no—
86C4×C139C2×SD1611yescharacteristic
87C4×C139#13511yescharacteristic
88C4×C139AGL(1,ℤ/8)11yescharacteristic
89C4×C139AGL(1,ℤ/8)11yescharacteristic
90Dic139—22no—
91Dic139—41no—
92Dic139—41no—
93Dic139—81no—
94C2×C139—82no—
95C2×C139#44911yescharacteristic
96C2×C139#45011yescharacteristic
97C2×C139#45511yescharacteristic
98D139—81no—
99C139#164211yescharacteristic, complemented, Sylow
100#1642—1391nomaximal, Sylow
101#550—1391no—
102#486—1391no—
103#475—1391no—
104#461—1391no—
105#331D13911yescharacteristic, complemented
106Q8⋊C8—1391no—
107D4⋊C8—1391no—
108C2×#41—2781no—
109C2×SD16—2781no—
110C4⋊Q8—1391no—
111#127—2781no—
112#127C2×D13911yescharacteristic
113#121—2782no—
114#121—2781no—
115C4×Q8—1391no—
116C4×D4—2781no—
117C4×D4—1391no—
118#106—2781no—
119C4⋊C8C2×D13911yescharacteristic
120C4⋊C8C2×D13911yescharacteristic
121#103—2781no—
122#103—2781no—
123#102—2782no—
124C4×C8—1391no—
125#41—5562no—
126#41—5562no—
127C2×Q8—2781no—
128C2×Q8—1391no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2782no—
132C2×D4—2782no—
133C2×D4—1391no—
134C2×D4D55612yes—
135C22×C4—2782no—
136C22×C4—2781no—
137SD16—5562no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—2781no—
141C4⋊C4—2781no—
142C4⋊C4—2781no—
143C4⋊C4—2781no—
144C4⋊C4—1391no—
145C4⋊C4—1391no—
146C22⋊C4—2782no—
147C22⋊C4—2781no—
148C42—2781no—
149C42C22×D13911yescharacteristic
150C23—22no—
151C23—2781no—
152Q8—2781no—
153Q8—5561no—
154Q8—5561no—
155Q8—1392no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—2781no—
162D4—2781no—
163D4—5564no—
164D4—11122no—
165C2×C4—2781no—
166C2×C4—2781no—
167C2×C4—2781no—
168C2×C4—5564no—
169C2×C4—5561no—
170C2×C4—5561no—
171C2×C4—5561no—
172C2×C4D4×D13911yescharacteristic
173C2×C4D4×D13911yescharacteristic
174C2×C4C2×D55611yescharacteristic
175C8—41no—
176C8—41no—
177C8—5561no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—5561no—
182C22—5561no—
183C22—5561no—
184C22#1798481211yescharacteristic
185C4—21no—
186C4—2782no—
187C4—5561no—
188C4—5561no—
189C4—11121no—
190C4SD16×D13911yescharacteristic
191C4#1798486311yescharacteristic
192C4#1798486611yescharacteristic
193C4#1798486611yescharacteristic
194C2—82no—
195C2—11121no—
196C2#2258109911yescharacteristic
197C2#2258110511yescharacteristic
198C2#2258113311yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#331×C139C2
socleC22×C139#120
prime radical#22581623C2
hypercenter#331D139
hypocenterC139#1642
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #22581299C2semidirect
3. #22581239C2semidirect
4. #22581159C2semidirect
5. #22580683C2semidirect
6. #22580680C2semidirect
7. #331×C139C2semidirect
54. Dic278SD16semidirect
99. C139#1642semidirect
105. #331D139semidirect

Maximal subgroups

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

subgroupindex
#225816232
#225812992
#225812392
#225811592
#225806832
#225806802
#331×C1392
#1642139