Finite Group Databasebeta

← #31808066

Subgroups — #31808066

Order 17792.

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

normal subgroups only

This group has 258 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#22581501C211yesmaximal, characteristic
2#22580925C212yesmaximal, complemented
3#22580747C212yesmaximal, complemented
4#22580746C211yesmaximal, characteristic, complemented
5#353×C139C211yesmaximal, characteristic, complemented
6C2×#14555784C411yescharacteristic, complemented
7C2×#14555784C2211yescharacteristic
8#17984842C411yescharacteristic, complemented
9#17984829C411yescharacteristic, complemented
10#17984829C2211yescharacteristic
11#17984813—22no—
12D4×Dic139—22no—
13#17984798—22no—
14C42×D139C411yescharacteristic, complemented
15#17984757C2212yes—
16#17984756—22no—
17#127×C139C2211yescharacteristic
18#99×C139C2212yes—
19#14555784—41no—
20#14555784—41no—
21#14555784—41no—
22#14555784—41no—
23C2×Dic278C2×C411yescharacteristic
24C2×Dic278C2×C411yescharacteristic
25C2×C22⋊D139—21no—
26C2×C22⋊D139D412yes—
27C22×Dic139—21no—
28C22×Dic139D412yes—
29C2×C4×D139—21no—
30C2×C4×D139C2×C411yescharacteristic
31C4⋊Dic139—22no—
32Dic139⋊C4—42no—
33C22⋊Dic139—22no—
34C22⋊Dic139—22no—
35C22⋊Dic139—22no—
36C4×Dic139—21no—
37C4×Dic139—42no—
38C4×Dic139C2×C411yescharacteristic
39C2×D4×C139—22no—
40C2×D4×C139C2×C411yescharacteristic
41C2×D4×C139C2311yescharacteristic
42C22⋊C4×C139—22no—
43C42×C139C2×C411yescharacteristic
44C22×D139C22⋊C411yescharacteristic
45Dic278—41no—
46Dic278—41no—
47C22⋊D139—42no—
48C22⋊D139—42no—
49C2×Dic139—22no—
50C2×Dic139—22no—
51C2×Dic139—21no—
52C2×Dic139—21no—
53C2×Dic139—41no—
54C2×Dic139—41no—
55C2×Dic139—42no—
56C2×Dic139C22⋊C412yes—
57C2×Dic139C22⋊C411yescharacteristic
58C4×D139—21no—
59C4×D139—21no—
60C4×D139—42no—
61C23×C139—21no—
62C23×C139C2×D412yes—
63D4×C139—41no—
64D4×C139—41no—
65D4×C139—44no—
66C2×C4×C139—21no—
67C2×C4×C139—42no—
68C2×C4×C139C22×C411yescharacteristic
69C22×C139—22no—
70C22×C139—42no—
71C22×C139—42no—
72C22×C139—41no—
73C22×C139C2×C22⋊C411yescharacteristic
74C2×D139—21no—
75C2×D139—41no—
76C4×C139—22no—
77C4×C139—21no—
78C4×C139—82no—
79Dic139—22no—
80Dic139—41no—
81Dic139—41no—
82Dic139—82no—
83Dic139#9911yescharacteristic
84Dic139#9911yescharacteristic
85C2×C139—21no—
86C2×C139—42no—
87C2×C139—81no—
88C2×C139C2×#9911yescharacteristic
89D139—41no—
90C139#212611yescharacteristic, complemented, Sylow
91#2126—1391nomaximal, Sylow
92#532—1391no—
93#410—1392no—
94#354—1392no—
95#353—1391no—
96#353D13911yescharacteristic, complemented
97C2×#41—1391no—
98C2×#41—1391no—
99C4⋊Q8—1391no—
100#127C2×D13911yescharacteristic
101#124—1391no—
102#124—1391no—
103#121—2782no—
104C4×D4—2782no—
105#117—2782no—
106C2×C42—1391no—
107#99—2782no—
108#99—1392no—
109#99C2×D13912yes—
110#41—5561no—
111#41—5561no—
112#41—5561no—
113#41—5561no—
114C2×Q8—1391no—
115C2×Q8—1391no—
116C2×D4—22no—
117C2×D4—2781no—
118C2×D4—1392no—
119C2×D4C4×D13911yescharacteristic
120C2×D4C22×D13911yescharacteristic
121C22×C4—2781no—
122C22×C4—2781no—
123C22×C4—1392no—
124C22×C4—1391no—
125C4⋊C4—2782no—
126C4⋊C4—5562no—
127C22⋊C4—22no—
128C22⋊C4—2782no—
129C22⋊C4—2782no—
130C22⋊C4—2782no—
131C42—2781no—
132C42—5562no—
133C42—1391no—
134C42C4×D13911yescharacteristic
135C23—21no—
136C23—1391no—
137C23D4×D13912yes—
138Q8—5561no—
139Q8—5561no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—5562no—
144D4—5562no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—2781no—
148C2×C4—2781no—
149C2×C4—2782no—
150C2×C4—2782no—
151C2×C4—2781no—
152C2×C4—2781no—
153C2×C4—5562no—
154C2×C4—5561no—
155C2×C4—5561no—
156C2×C4—5562no—
157C2×C4—1392no—
158C2×C4—1391no—
159C2×C4C2×C4×D13911yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—2781no—
165C22—5561no—
166C22C22⋊C4×D13911yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—2782no—
171C4—5561no—
172C4—5561no—
173C4—11122no—
174C4—1391no—
175C4—1391no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—5561no—
180C2#99×D13911yescharacteristic
subgroupG/H
centerC2#99×D139
commutatorC2×C4×C139C22×C4
FrattiniC2×D4C22×D139
Fitting#353×C139C2
socleC2×C139C2×#99
prime radical#22581501C2
cosocleC2×D4×C139C23
hypercenter#353D139
hypocenterC139#2126
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #22580925C2semidirect
3. #22580747C2semidirect
4. #22580746C2semidirect
5. #353×C139C2semidirect
6. C2×#14555784C4semidirect
8. #17984842C4semidirect
9. #17984829C4semidirect
14. C42×D139C4semidirect
90. C139#2126semidirect
96. #353D139semidirect

Maximal subgroups

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

subgroupindex
#225815012
#225809252
#225807472
#225807462
#353×C1392
#2126139