Finite Group Databasebeta

← #31807569

Subgroups — #31807569

Order 17792.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#22581579C211yesmaximal, characteristic, complemented
2#22580808C212yesmaximal
3#22580808C211yesmaximal, characteristic
4#22580719C212yesmaximal, complemented
5#342×C139C211yesmaximal, characteristic, complemented
6C24×D139C2211yescharacteristic
7#17984821—22no—
8#17984819—24no—
9C2×C22⋊Dic139C2211yescharacteristic
10C2×C22⋊Dic139C2212yes—
11C2×(C2×D139)⋊C4—24no—
12C2×(C2×D139)⋊C4—22no—
13C2×C22⋊C4×C139C2212yes—
14C2×C22⋊C4×C139C2211yescharacteristic
15C23×D139—22no—
16C23×D139—21no—
17C23×D139—21no—
18C23×D139—22no—
19C23×D139—44no—
20C23×D139Q812yescomplemented
21C2×Dic278—22no—
22C22×Dic139—21no—
23C22×Dic139D414yes—
24C4⋊Dic139—22no—
25Dic139⋊C4—24no—
26C22⋊Dic139—22no—
27C22⋊Dic139—22no—
28C22⋊Dic139—22no—
29(C2×D139)⋊C4—44no—
30(C2×D139)⋊C4—48no—
31C24×C139C2311yescharacteristic
32C22×C4×C139—22no—
33C22×C4×C139D412yes—
34C22⋊C4×C139—22no—
35C22⋊C4×C139—22no—
36C22⋊C4×C139—22no—
37C22×D139—28no—
38C22×D139—24no—
39C22×D139—24no—
40C22×D139—22no—
41C22×D139—44no—
42C22×D139—44no—
43C22×D139—48no—
44C22×D139—44no—
45C22×D139—42no—
46C22×D139—41no—
47C22×D139—42no—
48C22×D139—41no—
49Dic278—82no—
50C2×Dic139—24no—
51C2×Dic139—44no—
52C2×Dic139—42no—
53C2×Dic139—41no—
54C23×C139—42no—
55C23×C139C2×D412yes—
56C23×C139C2×D411yescharacteristic
57C23×C139C2×Q811yescharacteristic
58C23×C139#4111yescharacteristic
59C23×C139#4112yes—
60C2×C4×C139—22no—
61C2×C4×C139—42no—
62C2×C4×C139—44no—
63C2×C4×C139—42no—
64C22×C139—24no—
65C22×C139—22no—
66C22×C139—41no—
67C22×C139—41no—
68C22×C139—42no—
69C22×C139#12011yescharacteristic
70C22×C139C22⋊Q812yes—
71C22×C139C22⋊Q811yescharacteristic
72C22×C139#12412yes—
73C22×C139#12411yescharacteristic
74C2×D139—28no—
75C2×D139—24no—
76C2×D139—44no—
77C2×D139—48no—
78C2×D139—44no—
79C2×D139—42no—
80C2×D139—42no—
81C2×D139—44no—
82C4×C139—42no—
83C4×C139—82no—
84Dic139—44no—
85Dic139—81no—
86C2×C139—21no—
87C2×C139—22no—
88C2×C139—22no—
89C2×C139—21no—
90C2×C139#39311yescharacteristic
91C2×C139B(4,𝔽2)12yes—
92D139—44no—
93C139#202911yescharacteristic, complemented, Sylow
94#2029—1391nomaximal, Sylow
95#543—1391no—
96#379—1392no—
97#379—1391no—
98#342—1392no—
99#342D13911yescharacteristic, complemented
100C25—1391no—
101C22⋊Q8—2784no—
102C22⋊Q8—2782no—
103C2×C22⋊C4—2784no—
104C2×C22⋊C4—2782no—
105C2×C22⋊C4—1391no—
106C2×C22⋊C4—1392no—
107C2×C22⋊C4C2×D13912yes—
108C2×C22⋊C4C2×D13911yescharacteristic
109C24—2782no—
110C24—2781no—
111C24—2781no—
112C24—2782no—
113C24—5564no—
114C24—1392no—
115C24C22×D13911yescharacteristic
116C2×Q8—2782no—
117C22×C4—22no—
118C22×C4—2781no—
119C22×C4—1394no—
120C22×C4D55612yes—
121C4⋊C4—2784no—
122C4⋊C4—2782no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—2782no—
127C22⋊C4—2782no—
128C22⋊C4—2782no—
129C22⋊C4—5564no—
130C22⋊C4—5568no—
131C23—42no—
132C23—2788no—
133C23—2784no—
134C23—2784no—
135C23—2782no—
136C23—5564no—
137C23—5562no—
138C23—5564no—
139C23—5564no—
140C23—5568no—
141C23—5561no—
142C23—5562no—
143C23—5561no—
144C23D4×D13912yes—
145C23C2×D55611yescharacteristic
146C23Q8×D13911yescharacteristic
147C23#1455578411yescharacteristic
148C23#1455578512yes—
149Q8—11122no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—2784no—
155C2×C4—5564no—
156C2×C4—5562no—
157C2×C4—5561no—
158C22—24no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22—42no—
163C22—2788no—
164C22—2784no—
165C22—5568no—
166C22—5564no—
167C22—5564no—
168C22—5562no—
169C22—5562no—
170C22—5564no—
171C22#1798481211yescharacteristic
172C22#1798482012yes—
173C22#1798482211yescharacteristic
174C22#1798482812yes—
175C22#1798483011yescharacteristic
176C4—42no—
177C4—82no—
178C4—5564no—
179C4—11121no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—5564no—
185C2#2258086611yescharacteristic
186C2#2258114112yes—
subgroupG/H
centerC22#17984812
commutator, cosocleC24×C139C23
FrattiniC24C22×D139
Fitting#342×C139C2
socleC22×C139#120
prime radicalC24×D139C22
hypercenter#342D139
hypocenterC139#2029
LCSG ▷ C24×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #22581579C2semidirect
4. #22580719C2semidirect
5. #342×C139C2semidirect
20. C23×D139Q8semidirect
93. C139#2029semidirect
99. #342D139semidirect

Maximal subgroups

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

subgroupindex
#225815792
#225808082
#225807192
#342×C1392
#2029139