Finite Group Databasebeta

← #31807568

Subgroups — #31807568

Order 17792.

466 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 69 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#22580809C212yesmaximal
3#22580720C211yesmaximal, characteristic, complemented
4#22580719C212yesmaximal, complemented
5#379×C139C211yesmaximal, characteristic
6#17984821—22no—
7#17984819—24no—
8C2×C22⋊Dic139—24no—
9C2×C22⋊Dic139C2212yes—
10C2×C22⋊Dic139C2212yes—
11C25×C139C2211yescharacteristic
12C2×C22⋊C4×C139—22no—
13C2×C22⋊C4×C139C2211yescharacteristic
14C2×C22⋊C4×C139C2211yescharacteristic
15C2×Dic278—22no—
16C22×Dic139—22no—
17C22×Dic139D414yes—
18C4⋊Dic139—22no—
19Dic139⋊C4—24no—
20C22⋊Dic139—22no—
21C22⋊Dic139—22no—
22C22⋊Dic139—22no—
23C22⋊Dic139—22no—
24C22⋊Dic139—48no—
25C24×C139—22no—
26C24×C139—21no—
27C24×C139—22no—
28C24×C139—21no—
29C24×C139—44no—
30C24×C139Q812yescomplemented
31C24×C139C2311yescharacteristic
32C22×C4×C139—21no—
33C22×C4×C139D412yes—
34C22⋊C4×C139—22no—
35C22⋊C4×C139—22no—
36C22⋊C4×C139—44no—
37Dic278—82no—
38C2×Dic139—24no—
39C2×Dic139—44no—
40C2×Dic139—44no—
41C2×Dic139—42no—
42C23×C139—24no—
43C23×C139—28no—
44C23×C139—24no—
45C23×C139—22no—
46C23×C139—44no—
47C23×C139—42no—
48C23×C139—42no—
49C23×C139—44no—
50C23×C139—48no—
51C23×C139—44no—
52C23×C139—41no—
53C23×C139—42no—
54C23×C139—41no—
55C23×C139C2×D412yes—
56C23×C139C2×D411yescharacteristic
57C23×C139C2×Q811yescharacteristic
58C23×C139#4112yes—
59C23×C139#4111yescharacteristic
60C2×C4×C139—22no—
61C2×C4×C139—42no—
62C2×C4×C139—42no—
63C2×C4×C139—41no—
64C22×C139—22no—
65C22×C139—24no—
66C22×C139—24no—
67C22×C139—28no—
68C22×C139—41no—
69C22×C139—42no—
70C22×C139—41no—
71C22×C139—48no—
72C22×C139—44no—
73C22×C139—44no—
74C22×C139—42no—
75C22×C139—42no—
76C22×C139—44no—
77C22×C139#12011yescharacteristic
78C22×C139C22⋊Q812yes—
79C22×C139C22⋊Q811yescharacteristic
80C22×C139#12412yes—
81C22×C139#12411yescharacteristic
82C4×C139—42no—
83C4×C139—81no—
84Dic139—44no—
85Dic139—82no—
86C2×C139—22no—
87C2×C139—21no—
88C2×C139—22no—
89C2×C139—21no—
90C2×C139—44no—
91C2×C139#39311yescharacteristic
92C2×C139B(4,𝔽2)12yes—
93C139#202911yescharacteristic, complemented, Sylow
94#2029—1391nomaximal, Sylow
95#543—1391no—
96#379—1392no—
97#379D13911yescharacteristic
98#342—1392no—
99#342—1391no—
100C25C2×D13911yescharacteristic
101C22⋊Q8—2784no—
102C22⋊Q8—2782no—
103C2×C22⋊C4—22no—
104C2×C22⋊C4—2784no—
105C2×C22⋊C4—1392no—
106C2×C22⋊C4—1392no—
107C2×C22⋊C4C2×D13911yescharacteristic
108C2×C22⋊C4C2×D13911yescharacteristic
109C24—22no—
110C24—21no—
111C24—22no—
112C24—21no—
113C24—44no—
114C24Dic27812yescomplemented
115C24C22×D13911yescharacteristic
116C2×Q8—2782no—
117C22×C4—21no—
118C22×C4—2782no—
119C22×C4—1394no—
120C22×C4C22⋊D13912yes—
121C4⋊C4—2784no—
122C4⋊C4—2782no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—2782no—
127C22⋊C4—2782no—
128C22⋊C4—2782no—
129C22⋊C4—2782no—
130C22⋊C4—5568no—
131C23—24no—
132C23—28no—
133C23—24no—
134C23—22no—
135C23—44no—
136C23—42no—
137C23—42no—
138C23—44no—
139C23—48no—
140C23—44no—
141C23—41no—
142C23—42no—
143C23—41no—
144C23D4×D13912yes—
145C23C2×C22⋊D13911yescharacteristic
146C23C2×Dic27811yescharacteristic
147C23#1455578412yes—
148C23#1455578511yescharacteristic
149Q8—11122no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—2784no—
155C2×C4—5564no—
156C2×C4—5564no—
157C2×C4—5562no—
158C22—22no—
159C22—24no—
160C22—28no—
161C22—24no—
162C22—41no—
163C22—42no—
164C22—41no—
165C22—44no—
166C22—48no—
167C22—44no—
168C22—42no—
169C22—42no—
170C22—44no—
171C22#1798481011yescharacteristic
172C22#1798481912yes—
173C22#1798482111yescharacteristic
174C22#1798482812yes—
175C22#1798482911yescharacteristic
176C4—42no—
177C4—81no—
178C4—5564no—
179C4—11122no—
180C2—21no—
181C2—22no—
182C2—22no—
183C2—21no—
184C2—44no—
185C2#2258086511yescharacteristic
186C2#2258113912yes—
subgroupG/H
centerC22#17984810
commutator, cosocleC24×C139C23
FrattiniC24C22×D139
Fitting#379×C139C2
socleC22×C139#120
prime radicalC25×C139C22
hypercenter#379D139
hypocenterC139#2029
LCSG ▷ C24×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #22581579C2semidirect
3. #22580720C2semidirect
4. #22580719C2semidirect
30. C24×C139Q8semidirect
93. C139#2029semidirect
114. C24Dic278semidirect

Maximal subgroups

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

subgroupindex
#225815792
#225808092
#225807202
#225807192
#379×C1392
#2029139