Finite Group Databasebeta

← #31816534

Subgroups — #31816534

Order 17792.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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#22581510C211yesmaximal, characteristic
2#22581283C212yesmaximal
3#22581238C212yesmaximal, complemented
4#22581163C212yesmaximal, complemented
5#22581109C212yesmaximal
6#22581058C214yesmaximal, complemented
7#22581010C211yesmaximal, characteristic
8C2×C4×Q8×C139C211yesmaximal, characteristic
9C2×#14555775C2214yes—
10#17984842C2211yescharacteristic
11#17984842C2211yescharacteristic
12#17984834—21no—
13#17984821—21no—
14#17984821C2212yes—
15C4×Dic278—21no—
16C4×Dic278C2212yes—
17#17984801—21no—
18#17984773C2214yes—
19C4⋊(C139⋊C8)C2212yes—
20#17984766C2214yes—
21#17984765C2214yes—
22C22⋊(C139⋊C8)C2212yes—
23#17984753C2212yes—
24C22×Q8×C139C2211yescharacteristic
25C4×Q8×C139—21no—
26C4×Q8×C139—21no—
27C4×Q8×C139C2212yes—
28C4×Q8×C139C2212yes—
29C2×C4⋊C4×C139—21no—
30C2×C4⋊C4×C139C2211yescharacteristic
31C2×C42×C139—21no—
32C2×C42×C139C2211yescharacteristic
33C2×Dic278—21no—
34C2×Dic278C2312yes—
35#14555775—28no—
36C2×C139⋊C8C2314yes—
37C4⋊Dic139—21no—
38C4⋊Dic139—21no—
39C4⋊Dic139—21no—
40C4⋊Dic139C2312yes—
41Dic139⋊C4—22no—
42Dic139⋊C4—22no—
43C22⋊Dic139—22no—
44C4×Dic139—22no—
45C2×Q8×C139—24no—
46C2×Q8×C139—21no—
47C2×Q8×C139C2312yes—
48C22×C4×C139—21no—
49C22×C4×C139—21no—
50C22×C4×C139D411yescharacteristic
51C22×C4×C139D411yescharacteristic
52C22×C4×C139C2311yescharacteristic
53C4⋊C4×C139—22no—
54C4⋊C4×C139—22no—
55C4⋊C4×C139—21no—
56C4⋊C4×C139C2312yes—
57C42×C139—22no—
58C42×C139—22no—
59C42×C139D411yescharacteristic
60C42×C139D411yescharacteristic
61C42×C139C2311yescharacteristic
62C42×C139C2311yescharacteristic
63Dic278—24no—
64Dic278—42no—
65C2×Dic139—22no—
66C2×Dic139—22no—
67C139⋊C8—24no—
68C23×C139C2×D411yescharacteristic
69Q8×C139—24no—
70Q8×C139—22no—
71Q8×C139#4114yes—
72C2×C4×C139—24no—
73C2×C4×C139—22no—
74C2×C4×C139—22no—
75C2×C4×C139—22no—
76C2×C4×C139—22no—
77C2×C4×C139—22no—
78C2×C4×C139—42no—
79C2×C4×C139C2×D411yescharacteristic
80C2×C4×C139C2×D411yescharacteristic
81C2×C4×C139C2×D411yescharacteristic
82C2×C4×C139C2×D411yescharacteristic
83C2×C4×C139C2×D411yescharacteristic
84C2×C4×C139C2411yescharacteristic
85C22×C139—21no—
86C22×C139—21no—
87C22×C139#13712yes—
88C22×C139C22×D411yescharacteristic
89C4×C139—24no—
90C4×C139—21no—
91C4×C139—21no—
92C4×C139—21no—
93C4×C139—21no—
94C4×C139—42no—
95C4×C139#13712yes—
96C4×C139C2×#4112yes—
97Dic139—42no—
98Dic139—42no—
99C2×C139—22no—
100C2×C139#52511yescharacteristic
101C2×C139C2×#13711yescharacteristic
102C2×C139C2×#13711yescharacteristic
103C139#311311yescharacteristic, complemented, Sylow
104#3113—1391nomaximal, Sylow
105#533—1391no—
106C2×C4×Q8D13911yescharacteristic
107#483—1392no—
108#475—1392no—
109#462—1392no—
110#451—1392no—
111#441—1394no—
112#432—1391no—
113C22×Q8C2×D13911yescharacteristic
114C2×Q16—1394no—
115C4⋊Q8—1391no—
116C4⋊Q8—1391no—
117#125—2781no—
118C22⋊Q8—2781no—
119C22⋊Q8—1392no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—2781no—
123C4×Q8—1392no—
124C4×Q8C2×D13912yes—
125C4×Q8C2×D13912yes—
126#117—2781no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D13911yescharacteristic
129C2×C42—21no—
130C2×C42C2×D13911yescharacteristic
131#106—1394no—
132C4⋊C8—1392no—
133#103—1394no—
134#103—1394no—
135C22⋊C8—1392no—
136#97—1392no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—2781no—
140C2×Q8—1392no—
141C2×Q8C22×D13912yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D13911yescharacteristic
145C22×C4C22⋊D13911yescharacteristic
146C22×C4C22×D13911yescharacteristic
147Q16—2788no—
148C2×C8—1394no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—2782no—
153C4⋊C4—2782no—
154C4⋊C4—2781no—
155C4⋊C4—2781no—
156C4⋊C4—2781no—
157C4⋊C4—1392no—
158C4⋊C4C22×D13912yes—
159C22⋊C4—2782no—
160C42—22no—
161C42—22no—
162C42—2782no—
163C42C22⋊D13911yescharacteristic
164C42C22⋊D13911yescharacteristic
165C42C22×D13911yescharacteristic
166C42C22×D13911yescharacteristic
167C23C2×C22⋊D13911yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—2784no—
171Q8—5562no—
172Q8#1455578514yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—2782no—
181C2×C4—2782no—
182C2×C4C2×C22⋊D13911yescharacteristic
183C2×C4C2×C22⋊D13911yescharacteristic
184C2×C4C2×C22⋊D13911yescharacteristic
185C2×C4C2×C22⋊D13911yescharacteristic
186C2×C4C2×C22⋊D13911yescharacteristic
187C2×C4C23×D13911yescharacteristic
188C8—2784no—
189C22—21no—
190C22—21no—
191C22#1798487212yes—
192C22C22×C22⋊D13911yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—5562no—
200C4—5562no—
201C4#1798487312yes—
202C4C2×#1455578512yes—
203C2—22no—
204C2#2258146411yescharacteristic
205C2C2×#1798487211yescharacteristic
206C2C2×#1798487311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×C4×Q8×C139C2
socleC22×C139C22×D4
prime radicalC23×C139C2×D4
hypercenterC2×C4×Q8D139
hypocenterC139#3113
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #22581238C2semidirect
4. #22581163C2semidirect
6. #22581058C2semidirect
103. C139#3113semidirect

Maximal subgroups

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

subgroupindex
#225815102
#225812832
#225812382
#225811632
#225811092
#225810582
#225810102
C2×C4×Q8×C1392
#3113139