Finite Group Databasebeta

← #355×D139 #31808080

Subgroups — #355×D139 #31808080

Order 17792.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D139C211yesmaximal, characteristic
2#101×D139C212yesmaximal, complemented
3#22580750C211yesmaximal, characteristic, complemented
4#22580749C212yesmaximal, complemented
5#355×C139C211yesmaximal, characteristic, complemented
6C2×Q8×D139C2211yescharacteristic
7C2×D4×D139C411yescharacteristic
8M16×D139—22no—
9#17984831C2211yescharacteristic
10#17984830C411yescharacteristic
11#17984829C411yescharacteristic
12#17984828—22no—
13C22⋊C4×D139—22no—
14C42×D139C411yescharacteristic
15#17984761C2212yescomplemented
16#17984760—22no—
17#124×C139C2211yescharacteristic
18#101×C139C2212yescomplemented
19C23×D139—21no—
20C2×Dic278C2×C411yescharacteristic
21C2×Dic278D412yes—
22Q8×D139—41no—
23Q8×D139—41no—
24C2×D556C2×C411yescharacteristic
25C2×C22⋊D139—21no—
26D4×D139—41no—
27D4×D139—41no—
28C2×C4×D139—21no—
29C2×C4×D139C2×C411yescharacteristic
30C2×C4×D139D412yes—
31#14555769—22no—
32#14555768—42no—
33C8×D139—42no—
34C22⋊Dic139—22no—
35(C2×D139)⋊C4—22no—
36(C2×D139)⋊C4—22no—
37C4×Dic139—21no—
38C4×Dic139C2×C411yescharacteristic
39C2×Q8×C139C2311yescharacteristic
40C2×D4×C139C2×C411yescharacteristic
41M16×C139—22no—
42C22⋊C4×C139—22no—
43C42×C139C2×C411yescharacteristic
44C22×D139—21no—
45C22×D139—44no—
46C22×D139—41no—
47C22×D139—41no—
48C22×D139C22⋊C411yescharacteristic
49Dic278—41no—
50Dic278—42no—
51D556—41no—
52C22⋊D139—42no—
53C2×Dic139—21no—
54C2×Dic139C22⋊C411yescharacteristic
55C2×Dic139C22⋊C412yes—
56C4×D139—22no—
57C4×D139—22no—
58C4×D139—21no—
59C4×D139—21no—
60C4×D139—42no—
61C139⋊C8—42no—
62C23×C139—21no—
63Q8×C139—41no—
64D4×C139—41no—
65C2×C4×C139—21no—
66C2×C4×C139C22×C411yescharacteristic
67C2×C4×C139C2×D412yes—
68C8×C139—42no—
69C22×C139—42no—
70C22×C139—41no—
71C22×C139C2×C22⋊C411yescharacteristic
72C2×D139—22no—
73C2×D139—42no—
74C2×D139—41no—
75C2×D139—82no—
76C2×D139—82no—
77C2×D139#9911yescharacteristic
78C2×D139#9911yescharacteristic
79C4×C139—22no—
80C4×C139—21no—
81C4×C139—41no—
82Dic139—21no—
83Dic139—22no—
84Dic139—41no—
85C2×C139—21no—
86C2×C139—81no—
87C2×C139C2×#9911yescharacteristic
88D139—21no—
89D139—81no—
90D139#35512yesdirect product factor
91C139C2×#35511yescharacteristic, complemented, Sylow
92C2×#355—1391nomaximal, Sylow
93C2×#124—1391no—
94C2×#101—1392no—
95#355—1391no—
96#355—1392no—
97#355D13911yescharacteristic, direct product factor
98C22×Q8—1391no—
99C22×D4—1391no—
100C2×M16—2782no—
101#124—2782no—
102#124—1391no—
103#124—1391no—
104#124—1391no—
105#124C2×D13911yescharacteristic
106C2×C22⋊C4—2782no—
107C2×C42—1391no—
108#101—2782no—
109#101—1392no—
110#101C2×D13912yescomplemented
111C24—2781no—
112C2×Q8—5561no—
113C2×Q8—5561no—
114C2×Q8—1391no—
115C2×Q8—1392no—
116C2×Q8C22×D13911yescharacteristic
117C2×D4—2781no—
118C2×D4—5561no—
119C2×D4—5561no—
120C2×D4—1391no—
121C2×D4C4×D13911yescharacteristic
122C22×C4—2781no—
123C22×C4—1391no—
124C22×C4—1392no—
125M16—22no—
126M16—2782no—
127M16—5562no—
128C2×C8—5562no—
129C22⋊C4—22no—
130C22⋊C4—2782no—
131C22⋊C4—2782no—
132C22⋊C4—2782no—
133C42—2781no—
134C42—1391no—
135C42C4×D13911yescharacteristic
136C23—21no—
137C23—2781no—
138C23—5564no—
139C23—5561no—
140C23—5561no—
141C23—1391no—
142Q8—41no—
143Q8—5562no—
144Q8—5561no—
145D4—41no—
146D4—5561no—
147D4—5562no—
148C2×C4—21no—
149C2×C4—2782no—
150C2×C4—2782no—
151C2×C4—2781no—
152C2×C4—2781no—
153C2×C4—2781no—
154C2×C4—5562no—
155C2×C4—1391no—
156C2×C4—1392no—
157C2×C4C2×C4×D13911yescharacteristic
158C2×C4D4×D13912yes—
159C8—42no—
160C8—5562no—
161C22—42no—
162C22—41no—
163C22—2782no—
164C22—5562no—
165C22—5561no—
166C22—11122no—
167C22—11122no—
168C22—1391no—
169C22—1391no—
170C22C22⋊C4×D13911yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—2781no—
175C4—2782no—
176C4—5561no—
177C2—21no—
178C2—81no—
179C2—2781no—
180C2—11121no—
181C2—1392no—
182C2#99×D13911yescharacteristic
subgroupG/H
centerC2#99×D139
commutatorC2×C4×C139C22×C4
FrattiniC2×Q8C22×D139
Fitting#355×C139C2
socleC2×C139C2×#99
prime radicalC2×D4×D139C4
cosocleC2×Q8×C139C23
hypercenter#355D139
hypocenterC139C2×#355
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D139C2semidirect
3. #22580750C2semidirect
4. #22580749C2semidirect
5. #355×C139C2semidirect
15. #17984761C22semidirect
18. #101×C139C22semidirect
90. D139#355direct (N × H)
91. C139C2×#355semidirect
97. #355D139direct (N × H)
110. #101C2×D139semidirect

Maximal subgroups

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

subgroupindex
#124×D1392
#101×D1392
#225807502
#225807492
#355×C1392
C2×#355139