Finite Group Databasebeta

← #44487828

Subgroups — #44487828

Order 30592.

840 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C2×#21439922C213yesmaximal, complemented
2C2×(C22⋊D239)⋊C4C213yesmaximal, complemented
3#29504707C213yesmaximal, complemented
4#29504682C211yesmaximal, characteristic, complemented
5#29504681C213yesmaximal, complemented
6#29504617C211yesmaximal, characteristic, complemented
7#399×C239C211yesmaximal, characteristic, complemented
8C22×D956C2213yes—
9C22×C22⋊D239C2213yes—
10C23×Dic239C2211yescharacteristic
11C22×C4×D239C2213yes—
12#21439922—212no—
13(C22⋊D239)⋊C4—212no—
14C2×Dic239⋊C4C2213yes—
15C2×(C2×D239)⋊C4C2216yes—
16C2×(C2×D239)⋊C4C2213yes—
17C2×C4×Dic239C2213yes—
18C239⋊#95C2213yes—
19C2×C4⋊C4×C239C2213yes—
20C2×C22⋊C4×C239C2213yes—
21#95×C239C2211yescharacteristic
22C23×D239C2313yes—
23C2×D956—212no—
24C2×D956—26no—
25C2×C22⋊D239—26no—
26C2×C22⋊D239—26no—
27C2×C22⋊D239—26no—
28C22×Dic239—26no—
29C22×Dic239C2311yescharacteristic
30C22×Dic239C2313yes—
31C22×Dic239C2311yescharacteristic
32C2×C4×D239—26no—
33C2×C4×D239—212no—
34Dic239⋊C4—26no—
35(C2×D239)⋊C4—212no—
36(C2×D239)⋊C4—26no—
37C4×Dic239D4112yescomplemented
38C24×C239C2311yescharacteristic
39C22×C4×C239C2313yes—
40C22×C4×C239C2313yes—
41C4⋊C4×C239—26no—
42C22⋊C4×C239—26no—
43C22×D239—23no—
44C22×D239—26no—
45C22×D239—23no—
46C22×D239—26no—
47C22×D239#4116yes—
48D956—224no—
49C22⋊D239—224no—
50C2×Dic239—23no—
51C2×Dic239—23no—
52C2×Dic239—23no—
53C2×Dic239—44no—
54C2×Dic239C2×D416yes—
55C2×Dic239C2×D416yes—
56C4×D239—412no—
57C23×C239—23no—
58C23×C239—23no—
59C23×C239#4112yes—
60C23×C239C2411yescharacteristic
61C2×C4×C239—26no—
62C2×C4×C239—23no—
63C2×C4×C239—26no—
64C2×C4×C239C2×D416yes—
65C22×C239—26no—
66C22×C239—43no—
67C22×C239—41no—
68C22×C239C22×D413yes—
69C22×C239C2×#4113yes—
70C22×C239C2×#4111yescharacteristic
71C2×D239—26no—
72C2×D239—212no—
73C2×D239—43no—
74C2×D239—46no—
75C2×D239—43no—
76C4×C239—26no—
77C4×C239—43no—
78Dic239—26no—
79Dic239—41no—
80Dic239#12714yes—
81C2×C239—42no—
82C2×C239#52513yes—
83C2×C239#52513yes—
84C2×C239C2×#12711yescharacteristic
85D239—46no—
86C239#239711yescharacteristic, complemented, Sylow
87#2397—2391nomaximal, Sylow
88C2×C4×D4—2393no—
89C2×C4×D4—2393no—
90#399—2393no—
91#399D23911yescharacteristic, complemented
92#392—2393no—
93#392—2391no—
94#376—2391no—
95C22×D4—2393no—
96C22×D4—2393no—
97C23×C4—2391no—
98C23×C4—2393no—
99C4×D4—47812no—
100C4×D4—47812no—
101C2×C4⋊C4—2393no—
102C2×C4⋊C4C2×D23913yes—
103C2×C22⋊C4—2396no—
104C2×C22⋊C4—2393no—
105C2×C22⋊C4C2×D23913yes—
106C2×C42—2393no—
107#95—2393no—
108#95C2×D23911yescharacteristic
109C24—2393no—
110C24C22×D23911yescharacteristic
111C2×D4—47812no—
112C2×D4—4786no—
113C2×D4—4786no—
114C2×D4—4786no—
115C2×D4—4786no—
116C22×C4—4786no—
117C22×C4—47812no—
118C22×C4—4786no—
119C22×C4—2391no—
120C22×C4—2393no—
121C22×C4—2391no—
122C22×C4C22×D23913yes—
123C22×C4C22×D23913yes—
124C4⋊C4—26no—
125C4⋊C4—4786no—
126C22⋊C4—26no—
127C22⋊C4—47812no—
128C22⋊C4—4786no—
129C42—23912no—
130C23—23no—
131C23—23no—
132C23—4786no—
133C23—4783no—
134C23—4783no—
135C23—4786no—
136C23—2396no—
137C23#1683854912yes—
138C23C23×D23911yescharacteristic
139D4—47824no—
140D4—47824no—
141C2×C4—26no—
142C2×C4—23no—
143C2×C4—26no—
144C2×C4—95612no—
145C2×C4—9564no—
146C2×C4—4783no—
147C2×C4—4783no—
148C2×C4—4783no—
149C2×C4—2396no—
150C2×C4—2396no—
151C2×C4D4×D23916yes—
152C22—26no—
153C22—43no—
154C22—41no—
155C22—9563no—
156C22—9566no—
157C22—9563no—
158C22—47812no—
159C22—4786no—
160C22C2×D4×D23913yes—
161C22#41×D23913yes—
162C22C2×#1683854911yescharacteristic
163C4—26no—
164C4—43no—
165C4—9561no—
166C4—4786no—
167C4—2394no—
168C2—42no—
169C2—9566no—
170C2#2950528013yes—
171C2#2950528513yes—
172C2#127×D23911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutator, socle, cosocleC23×C239C24
Fitting#399×C239C2
hypercenter#399D239
hypocenterC239#2397
LCSG ▷ C23×C239 ▷ C239
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#21439922C2semidirect
2. C2×(C22⋊D239)⋊C4C2semidirect
3. #29504707C2semidirect
4. #29504682C2semidirect
5. #29504681C2semidirect
6. #29504617C2semidirect
7. #399×C239C2semidirect
37. C4×Dic239D4semidirect
86. C239#2397semidirect
91. #399D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399222
C2×(C22⋊D239)⋊C42
#295047072
#295046822
#295046812
#295046172
#399×C2392
#2397239