Finite Group Databasebeta

← #31805701

Subgroups — #31805701

Order 17792.

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

normal subgroups only

This group has 206 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#22581707C211yesmaximal, characteristic, complemented
2#22581340C211yesmaximal, characteristic
3#22581317C211yesmaximal, characteristic, complemented
4#22580695C211yesmaximal, characteristic, complemented
5#22580694C211yesmaximal, characteristic, complemented
6#22580692C211yesmaximal, characteristic, complemented
7#490×C139C211yesmaximal, characteristic, complemented
8C2×#14555773—21no—
9C2×#14555770—21no—
10#17984841—21no—
11#17984837—21no—
12#17984837—21no—
13#17984834C2211yescharacteristic
14#17984830C2211yescharacteristic
15#17984827—21no—
16#17984822—21no—
17#17984820—21no—
18#17984763—21no—
19#17984763—21no—
20#17984753C2211yescharacteristic
21#17984753C2211yescharacteristic
22#127×C139C2211yescharacteristic
23#125×C139C2211yescharacteristic
24#102×C139—21no—
25#102×C139—21no—
26#97×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278D411yescharacteristic
29C2×D556D411yescharacteristic
30C2×C4×D139—21no—
31#14555773—42no—
32#14555770—42no—
33C2×C139⋊C8—21no—
34C2×C139⋊C8—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139D411yescharacteristic
37C4⋊Dic139D411yescharacteristic
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40Dic139⋊C4—21no—
41(C2×D139)⋊C4—21no—
42(C2×D139)⋊C4—21no—
43(C2×D139)⋊C4—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46C4×Dic139—21no—
47C2×D4×C139—21no—
48C2×D4×C139—21no—
49C2×D4×C139—21no—
50C2×C8×C139—21no—
51C4⋊C4×C139—21no—
52C4⋊C4×C139—21no—
53C4⋊C4×C139D411yescharacteristic
54C4⋊C4×C139D411yescharacteristic
55C42×C139C2311yescharacteristic
56C22×D139—21no—
57Dic278—41no—
58Dic278—81no—
59D556—41no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C4×D139—81no—
64C139⋊C8—22no—
65C139⋊C8—41no—
66C23×C139—41no—
67D4×C139—42no—
68D4×C139—42no—
69D4×C139—41no—
70D4×C139—41no—
71C2×C4×C139—21no—
72C2×C4×C139—21no—
73C2×C4×C139C2×D411yescharacteristic
74C2×C4×C139C2×D411yescharacteristic
75C2×C4×C139C2×D411yescharacteristic
76C8×C139—41no—
77C22×C139—81no—
78C22×C139—81no—
79C22×C139—81no—
80C22×C139#12011yescharacteristic
81C2×D139—41no—
82C2×D139—41no—
83C2×D139—41no—
84C4×C139—21no—
85C4×C139—21no—
86C4×C139—21no—
87C4×C139—41no—
88C4×C139—41no—
89Dic139—41no—
90Dic139—41no—
91Dic139—41no—
92C2×C139—161no—
93C2×C139#45311yescharacteristic
94C2×C139#45411yescharacteristic
95C2×C139#45411yescharacteristic
96D139—81no—
97C139#165711yescharacteristic, complemented, Sylow
98#1657—1391nomaximal, Sylow
99#563—1391no—
100#496—1391no—
101#490—1391no—
102#490D13911yescharacteristic, complemented
103#330—1391no—
104#330—1391no—
105#329—1391no—
106C2×SD16—2781no—
107C2×D8—2781no—
108C4⋊Q8—2781no—
109#127C2×D13911yescharacteristic
110#126—2781no—
111#126—2781no—
112#125—1391no—
113#125C2×D13911yescharacteristic
114#124—1391no—
115#123—2781no—
116C22⋊Q8—2781no—
117C22⋊Q8—2781no—
118#102—21no—
119#102—21no—
120#102—2781no—
121#102—2781no—
122#97—1391no—
123#97—1391no—
124#97C2×D13911yescharacteristic
125C2×Q8—2781no—
126C2×Q8—1391no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—1391no—
131C22×C4—2781no—
132SD16—5562no—
133D8—5562no—
134C2×C8—21no—
135C2×C8—2781no—
136C2×C8—2781no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—2781no—
140C4⋊C4—2781no—
141C4⋊C4—2781no—
142C4⋊C4—2781no—
143C4⋊C4—1391no—
144C4⋊C4—1391no—
145C4⋊C4C22⋊D13911yescharacteristic
146C4⋊C4C22⋊D13911yescharacteristic
147C22⋊C4—2781no—
148C22⋊C4—2781no—
149C22⋊C4—2781no—
150C22⋊C4—2781no—
151C22⋊C4—2781no—
152C42—2781no—
153C42C22×D13911yescharacteristic
154C23—41no—
155C23—2781no—
156Q8—5561no—
157Q8—11121no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—5561no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—2781no—
166C2×C4—2781no—
167C2×C4—2781no—
168C2×C4—11121no—
169C2×C4D4×D13911yescharacteristic
170C2×C4D4×D13911yescharacteristic
171C2×C4C2×C22⋊D13911yescharacteristic
172C8—41no—
173C8—2782no—
174C8—5561no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—5561no—
179C22—5561no—
180C22—5561no—
181C22#1798481011yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—5561no—
188C4—5561no—
189C4—5561no—
190C2—161no—
191C2—11121no—
192C2#2258111911yescharacteristic
193C2#2258112411yescharacteristic
194C2#2258112511yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#490×C139C2
socleC22×C139#120
prime radical#22581340C2
hypercenter#490D139
hypocenterC139#1657
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #22581707C2semidirect
3. #22581317C2semidirect
4. #22580695C2semidirect
5. #22580694C2semidirect
6. #22580692C2semidirect
7. #490×C139C2semidirect
97. C139#1657semidirect
102. #490D139semidirect

Maximal subgroups

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

subgroupindex
#225817072
#225813402
#225813172
#225806952
#225806942
#225806922
#490×C1392
#1657139