Finite Group Databasebeta

← #31808068

Subgroups — #31808068

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#22581502C211yesmaximal, characteristic
2#22580925C212yesmaximal, complemented
3#22580748C211yesmaximal, characteristic, complemented
4#22580745C212yesmaximal, complemented
5#354×C139C211yesmaximal, characteristic, complemented
6C2×#14555786C411yescharacteristic, complemented
7C2×#14555784C2211yescharacteristic
8#17984840C411yescharacteristic, complemented
9#17984838C2211yescharacteristic
10#17984830C411yescharacteristic, complemented
11#17984815—22no—
12(C22⋊D139)⋊C4—22no—
13#17984798—22no—
14C42×D139C411yescharacteristic, complemented
15#17984757C2212yes—
16#17984756—22no—
17#124×C139C2211yescharacteristic
18#99×C139C2212yes—
19#14555786—41no—
20#14555786—41no—
21#14555784—41no—
22#14555784—41no—
23C2×Dic278C2×C411yescharacteristic
24C2×D556—21no—
25C2×D556C2×C411yescharacteristic
26C2×C22⋊D139—22no—
27C2×C22⋊D139D412yes—
28C22×Dic139D412yes—
29C2×C4×D139—21no—
30C2×C4×D139—21no—
31C2×C4×D139C2×C411yescharacteristic
32Dic139⋊C4—22no—
33Dic139⋊C4—42no—
34C22⋊Dic139—22no—
35(C2×D139)⋊C4—22no—
36C4×Dic139—21no—
37C4×Dic139—42no—
38C4×Dic139C2×C411yescharacteristic
39C2×Q8×C139C2×C411yescharacteristic
40C2×D4×C139C2311yescharacteristic
41C22⋊C4×C139—22no—
42C22⋊C4×C139—22no—
43C42×C139C2×C411yescharacteristic
44C22×D139—21no—
45C22×D139C22⋊C411yescharacteristic
46Dic278—41no—
47D556—41no—
48D556—42no—
49C22⋊D139—42no—
50C22⋊D139—44no—
51C2×Dic139—21no—
52C2×Dic139—22no—
53C2×Dic139—22no—
54C2×Dic139—42no—
55C2×Dic139C22⋊C412yes—
56C2×Dic139C22⋊C411yescharacteristic
57C4×D139—21no—
58C4×D139—21no—
59C4×D139—42no—
60C4×D139—41no—
61C4×D139—41no—
62C23×C139C2×D412yes—
63Q8×C139—41no—
64D4×C139—41no—
65C2×C4×C139—21no—
66C2×C4×C139—21no—
67C2×C4×C139—42no—
68C2×C4×C139C22×C411yescharacteristic
69C22×C139—22no—
70C22×C139—42no—
71C22×C139C2×C22⋊C411yescharacteristic
72C2×D139—21no—
73C2×D139—41no—
74C2×D139—42no—
75C2×D139—41no—
76C4×C139—21no—
77C4×C139—41no—
78C4×C139—41no—
79C4×C139—82no—
80Dic139—22no—
81Dic139—22no—
82Dic139—82no—
83Dic139#9911yescharacteristic
84Dic139#9911yescharacteristic
85C2×C139—21no—
86C2×C139—42no—
87C2×C139C2×#9911yescharacteristic
88D139—41no—
89D139—81no—
90C139#212611yescharacteristic, complemented, Sylow
91#2126—1391nomaximal, Sylow
92#532—1391no—
93#410—1392no—
94#354—1391no—
95#354D13911yescharacteristic, complemented
96#353—1392no—
97C2×#41—1391no—
98C2×#41—1391no—
99C4⋊Q8—1391no—
100#127—1391no—
101#124—1391no—
102#124C2×D13911yescharacteristic
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×Q8C4×D13911yescharacteristic
116C2×D4—2781no—
117C2×D4—2782no—
118C2×D4—1392no—
119C2×D4—1391no—
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—22no—
129C22⋊C4—2782no—
130C22⋊C4—2782no—
131C42—2781no—
132C42—5562no—
133C42—1391no—
134C42C4×D13911yescharacteristic
135C23—2781no—
136C23—1391no—
137C23D4×D13912yes—
138Q8—41no—
139Q8—5561no—
140D4—41no—
141D4—5561no—
142D4—5562no—
143D4—5562no—
144D4—5564no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2781no—
149C2×C4—2781no—
150C2×C4—2781no—
151C2×C4—2782no—
152C2×C4—2782no—
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—2781no—
163C22—5561no—
164C22—5562no—
165C22—5561no—
166C22C22⋊C4×D13911yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—2782no—
172C4—2782no—
173C4—11122no—
174C4—1391no—
175C4—1391no—
176C2—21no—
177C2—42no—
178C2—5561no—
179C2—11121no—
180C2#99×D13911yescharacteristic
subgroupG/H
centerC2#99×D139
commutatorC2×C4×C139C22×C4
FrattiniC2×D4C22×D139
Fitting#354×C139C2
socleC2×C139C2×#99
prime radical#22581502C2
cosocleC2×D4×C139C23
hypercenter#354D139
hypocenterC139#2126
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #22580925C2semidirect
3. #22580748C2semidirect
4. #22580745C2semidirect
5. #354×C139C2semidirect
6. C2×#14555786C4semidirect
8. #17984840C4semidirect
10. #17984830C4semidirect
14. C42×D139C4semidirect
90. C139#2126semidirect
95. #354D139semidirect

Maximal subgroups

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

subgroupindex
#225815022
#225809252
#225807482
#225807452
#354×C1392
#2126139