Finite Group Databasebeta

← #31817874

Subgroups — #31817874

Order 17792.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#22581570C212yesmaximal, complemented
2#22581241C212yesmaximal, complemented
3#22581237C212yesmaximal, complemented
4#22581211C211yesmaximal, characteristic, complemented
5#22581180C212yesmaximal, complemented
6#22581174C212yesmaximal, complemented
7#22581166C212yesmaximal, complemented
8#22580981C211yesmaximal, characteristic, complemented
9#469×C139C211yesmaximal, characteristic
10C2×Dic556C2211yescharacteristic
11C2×#14555773C2212yes—
12C22×C139⋊C8C2211yescharacteristic
13#17984841C2212yes—
14#17984835—22no—
15#17984829—22no—
16#17984829C2212yes—
17#17984823—22no—
18#17984821C2212yes—
19#17984819—22no—
20#17984807C2212yes—
21D4×Dic139C2212yes—
22#17984801C2211yescharacteristic
23#17984774C2211yescharacteristic
24#17984773C2212yes—
25Dic139⋊C8C2212yes—
26Dic139⋊C8C2212yes—
27#17984767C2212yes—
28#17984765C2212yes—
29#17984763C2212yes—
30C2×D8×C139C2211yescharacteristic
31C2×M16×C139C2211yescharacteristic
32#121×C139C2212yes—
33#106×C139C2211yescharacteristic
34#102×C139C2212yes—
35C2×Dic278—22no—
36C2×Dic278C2312yes—
37C22×Dic139—22no—
38Dic556—41no—
39#14555773—42no—
40C2×C139⋊C8—41no—
41C2×C139⋊C8C2312yes—
42C4⋊Dic139D412yes—
43C4⋊Dic139C2312yes—
44Dic139⋊C4—22no—
45Dic139⋊C4—22no—
46Dic139⋊C4—22no—
47C22⋊Dic139—22no—
48C22⋊Dic139—22no—
49C22⋊Dic139—22no—
50C22⋊Dic139—22no—
51C22⋊Dic139D411yescharacteristic
52C22⋊Dic139D411yescharacteristic
53C4×Dic139—22no—
54C4×Dic139C2312yes—
55C2×D4×C139—22no—
56C2×D4×C139C2312yes—
57C22×C4×C139C2311yescharacteristic
58D8×C139—41no—
59M16×C139—41no—
60C2×C8×C139C2311yescharacteristic
61C2×C8×C139C2311yescharacteristic
62C4⋊C4×C139C2312yes—
63C22⋊C4×C139—22no—
64Dic278—22no—
65Dic278—22no—
66Dic278—82no—
67C2×Dic139—22no—
68C2×Dic139—22no—
69C2×Dic139—82no—
70C2×Dic139C2×D412yes—
71C2×Dic139C2×D412yes—
72C139⋊C8—22no—
73C23×C139—22no—
74C23×C139C2×D411yescharacteristic
75D4×C139—22no—
76D4×C139—22no—
77D4×C139—82no—
78C2×C4×C139—21no—
79C2×C4×C139—21no—
80C2×C4×C139—22no—
81C2×C4×C139C2×D411yescharacteristic
82C2×C4×C139C2411yescharacteristic
83C8×C139—21no—
84C8×C139—21no—
85C22×C139—21no—
86C22×C139—22no—
87C22×C139—42no—
88C22×C139—42no—
89C22×C139—42no—
90C22×C139C22×D411yescharacteristic
91C4×C139—21no—
92C4×C139—42no—
93C4×C139H(5,𝔽2)11yescharacteristic
94C4×C1392−1+411yescharacteristic
95Dic139—22no—
96Dic139—22no—
97Dic139—42no—
98Dic139—42no—
99C2×C139—41no—
100C2×C139—82no—
101C2×C139#53711yescharacteristic
102C2×C139#57712yes—
103C139#326311yescharacteristic, complemented, Sylow
104#3263—1391nomaximal, Sylow
105#542—1392no—
106#476—1392no—
107#475—1392no—
108#470—1391no—
109#469D13911yescharacteristic
110#465—1392no—
111#464—1392no—
112#463—1392no—
113#424—1391no—
114C2×Q16—1391no—
115C2×SD16—1392no—
116C2×D8C2×D13911yescharacteristic
117C2×M16C2×D13911yescharacteristic
118C22×C8—1391no—
119C4⋊Q8—1392no—
120#126—2782no—
121#124—2782no—
122#124—1392no—
123#123—2782no—
124C22⋊Q8—2782no—
125C22⋊Q8—1392no—
126#121C2×D13912yes—
127C4×Q8—1392no—
128C4×D4—1392no—
129#117—1391no—
130#106—1391no—
131#106—1392no—
132#106C2×D13911yescharacteristic
133C4⋊C8—1392no—
134C4⋊C8—1392no—
135#103—1392no—
136#103—1392no—
137#102—1392no—
138#102C2×D13912yes—
139C2×Q8—2782no—
140C2×Q8—1392no—
141C2×D4—22no—
142C2×D4C22×D13912yes—
143C22×C4—2782no—
144C22×C4C22×D13911yescharacteristic
145Q16—5561no—
146SD16—5562no—
147D8—41no—
148M16—41no—
149C2×C8—5561no—
150C2×C8—1392no—
151C2×C8C22×D13911yescharacteristic
152C2×C8C22×D13911yescharacteristic
153C4⋊C4—2782no—
154C4⋊C4—2782no—
155C4⋊C4—2782no—
156C4⋊C4—1392no—
157C4⋊C4—1392no—
158C4⋊C4C22×D13912yes—
159C22⋊C4—22no—
160C22⋊C4—2782no—
161C22⋊C4—2782no—
162C22⋊C4—2782no—
163C22⋊C4—2782no—
164C22⋊C4—1391no—
165C22⋊C4—1391no—
166C42—2782no—
167C42—1392no—
168C23—22no—
169C23D4×D13911yescharacteristic
170Q8—2782no—
171Q8—2782no—
172Q8—11122no—
173D4—22no—
174D4—22no—
175D4—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—2782no—
180C2×C4—2782no—
181C2×C4—11122no—
182C2×C4—1392no—
183C2×C4—1392no—
184C2×C4D4×D13911yescharacteristic
185C2×C4C23×D13911yescharacteristic
186C8—21no—
187C8—21no—
188C8—2782no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D13911yescharacteristic
195C4—21no—
196C4—42no—
197C4—2782no—
198C4—2782no—
199C4—5562no—
200C4—5562no—
201C4#1798488711yescharacteristic
202C4#1798488911yescharacteristic
203C2—41no—
204C2—82no—
205C2#2258153011yescharacteristic
206C2#2258176312yes—
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting, prime radical#469×C139C2
socleC22×C139C22×D4
hypercenter#469D139
hypocenterC139#3263
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #22581570C2semidirect
2. #22581241C2semidirect
3. #22581237C2semidirect
4. #22581211C2semidirect
5. #22581180C2semidirect
6. #22581174C2semidirect
7. #22581166C2semidirect
8. #22580981C2semidirect
103. C139#3263semidirect

Maximal subgroups

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

subgroupindex
#225815702
#225812412
#225812372
#225812112
#225811802
#225811742
#225811662
#225809812
#469×C1392
#3263139