Finite Group Databasebeta

← #31816751

Subgroups — #31816751

Order 17792.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#22581509C211yesmaximal, characteristic, complemented
2#22581504C211yesmaximal, characteristic
3#22581321C211yesmaximal, characteristic, complemented
4#22581319C211yesmaximal, characteristic, complemented
5#22581318C211yesmaximal, characteristic, complemented
6#22581314C214yesmaximal, complemented
7#22580948C214yesmaximal, complemented
8#97×D139C211yesmaximal, characteristic, complemented
9#491×C139C211yesmaximal, characteristic, complemented
10C2×#14555786C2212yes—
11C2×C8×D139C2212yes—
12#17984841C2212yes—
13#17984839C2211yescharacteristic
14#17984834C2211yescharacteristic
15#17984831C2212yes—
16#17984820—22no—
17#17984817—22no—
18#17984807—22no—
19#17984804—22no—
20#17984800C2212yes—
21C42×D139C2211yescharacteristic
22#17984766C2214yes—
23#17984764C2214yes—
24#17984762C2214yes—
25#17984753C2211yescharacteristic
26#17984752C2212yes—
27C4⋊Q8×C139C2211yescharacteristic
28#125×C139C2211yescharacteristic
29#103×C139C2214yes—
30#97×C139C2211yescharacteristic
31#14555786—28no—
32C2×Dic278—22no—
33C2×D556—22no—
34C2×D556—22no—
35C2×D556C2312yes—
36C2×C4×D139—22no—
37C2×C4×D139D412yes—
38C2×C4×D139C2311yescharacteristic
39C2×C139⋊C8C2312yes—
40C8×D139—24no—
41C4⋊Dic139C2312yes—
42Dic139⋊C4—22no—
43Dic139⋊C4—22no—
44(C2×D139)⋊C4—22no—
45(C2×D139)⋊C4—24no—
46C4×Dic139—22no—
47C4×Dic139D412yes—
48C4×Dic139C2311yescharacteristic
49C2×Q8×C139C2312yes—
50C2×C8×C139C2312yes—
51C4⋊C4×C139—22no—
52C4⋊C4×C139—22no—
53C4⋊C4×C139C2312yes—
54C42×C139C2311yescharacteristic
55C22×D139—22no—
56C22×D139C2×D411yescharacteristic
57Dic278—44no—
58D556—24no—
59D556—44no—
60D556—44no—
61C2×Dic139—22no—
62C2×Dic139C2×D412yes—
63C2×Dic139C2×D411yescharacteristic
64C4×D139—42no—
65C4×D139—44no—
66C4×D139#4114yes—
67C139⋊C8—22no—
68Q8×C139—24no—
69C2×C4×C139—22no—
70C2×C4×C139—22no—
71C2×C4×C139C2×D412yes—
72C2×C4×C139C2411yescharacteristic
73C8×C139—22no—
74C22×C139C22×D411yescharacteristic
75C2×D139—22no—
76C2×D139—42no—
77C2×D139—44no—
78C2×D139#12412yes—
79C4×C139—22no—
80C4×C139—42no—
81C4×C139—42no—
82C4×C139C2×#4112yes—
83Dic139—22no—
84Dic139—42no—
85Dic139#12412yes—
86C2×C139C2×#12411yescharacteristic
87C2×C139#57512yes—
88D139—22no—
89D139—82no—
90C139#313511yescharacteristic, complemented, Sylow
91#3135—1391nomaximal, Sylow
92#533—1391no—
93#532—1391no—
94#491—1391no—
95#491D13911yescharacteristic, complemented
96#490—1391no—
97#490—1391no—
98#489—1394no—
99#416—1394no—
100C2×#97—1391no—
101C2×#41—1392no—
102C22×C8—1392no—
103C4⋊Q8—1392no—
104C4⋊Q8C2×D13911yescharacteristic
105#127—1391no—
106#125—1391no—
107#125C2×D13911yescharacteristic
108#124—1392no—
109C22⋊Q8—2782no—
110#121—2782no—
111C4×Q8—2782no—
112C4×D4—2782no—
113#117—1392no—
114C2×C42—1391no—
115#103—1394no—
116#103C2×D13914yes—
117#102—1394no—
118#102—1394no—
119#97—1392no—
120#97—1391no—
121#97C2×D13911yescharacteristic
122#41—2788no—
123C2×Q8—2782no—
124C2×Q8C22×D13912yes—
125C2×D4—2782no—
126C2×D4—2782no—
127C2×D4—1392no—
128C22×C4—2782no—
129C22×C4—1392no—
130C22×C4—1391no—
131C2×C8—2784no—
132C2×C8—1392no—
133C2×C8C22×D13912yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—2782no—
137C4⋊C4—2782no—
138C4⋊C4—1392no—
139C4⋊C4C22×D13912yes—
140C22⋊C4—2782no—
141C22⋊C4—2784no—
142C42—2782no—
143C42—1392no—
144C42—1391no—
145C42C22×D13911yescharacteristic
146C23—2782no—
147C23—1391no—
148Q8—24no—
149Q8—5564no—
150D4—2784no—
151D4—5564no—
152D4—5564no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—2782no—
156C2×C4—5562no—
157C2×C4—5564no—
158C2×C4—1392no—
159C2×C4—1391no—
160C2×C4—1394no—
161C2×C4D4×D13912yes—
162C2×C4C23×D13911yescharacteristic
163C8—22no—
164C8—2782no—
165C22—2782no—
166C22—5562no—
167C22—5564no—
168C22—1392no—
169C22C2×D4×D13911yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—2782no—
174C4—5562no—
175C4—1392no—
176C4#41×D13912yes—
177C2—2782no—
178C2—11122no—
179C2#124×D13911yescharacteristic
180C2#2258175212yes—
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#491×C139C2
socleC22×C139C22×D4
prime radical#22581504C2
hypercenter#491D139
hypocenterC139#3135
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #22581509C2semidirect
3. #22581321C2semidirect
4. #22581319C2semidirect
5. #22581318C2semidirect
6. #22581314C2semidirect
7. #22580948C2semidirect
8. #97×D139C2semidirect
9. #491×C139C2semidirect
90. C139#3135semidirect
95. #491D139semidirect

Maximal subgroups

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

subgroupindex
#225815092
#225815042
#225813212
#225813192
#225813182
#225813142
#225809482
#97×D1392
#491×C1392
#3135139