Finite Group Databasebeta

← #44483533

Subgroups — #44483533

Order 30592.

280 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 53 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#29505334C211yesmaximal, characteristic
2#29505085C212yesmaximal, complemented
3#29504505C212yesmaximal, complemented
4#29504496C211yesmaximal, characteristic, complemented
5#397×C239C211yesmaximal, characteristic, complemented
6C22×C22⋊D239—21no—
7#21439944—22no—
8#21439934—21no—
9#21439934C2212yes—
10#21439930—22no—
11#21439893—22no—
12#21439880—22no—
13C22⋊(C239⋊C8)C2212yescomplemented
14C2×C4⋊C4×C239C2211yescharacteristic, complemented
15C2×C22⋊C4×C239—21no—
16C2×C22⋊C4×C239C2211yescharacteristic
17#95×C239—21no—
18#95×C239C2211yescharacteristic, complemented
19C23×D239—21no—
20C2×D956—21no—
21C2×D956D412yes—
22C2×C22⋊D239—22no—
23C2×C22⋊D239—22no—
24C2×C22⋊D239—42no—
25C2×C22⋊D239—42no—
26C22×Dic239—21no—
27C2×C239⋊C8—22no—
28C4⋊Dic239—21no—
29C4⋊Dic239D412yes—
30(C2×D239)⋊C4—22no—
31(C2×D239)⋊C4—22no—
32C24×C239D411yescharacteristic
33C22×C4×C239—21no—
34C22×C4×C239—21no—
35C22×C4×C239D411yescharacteristic
36C22×C4×C239C2311yescharacteristic
37C4⋊C4×C239—22no—
38C22⋊C4×C239—22no—
39C22⋊C4×C239—42no—
40C22×D239—22no—
41C22×D239—42no—
42C22×D239—81no—
43C22×D239—81no—
44D956—42no—
45D956—81no—
46C22⋊D239—44no—
47C22⋊D239—42no—
48C22⋊D239—42no—
49C2×Dic239—22no—
50C2×Dic239—42no—
51C239⋊C8—42no—
52C23×C239—21no—
53C23×C239—21no—
54C23×C239—41no—
55C23×C239—41no—
56C23×C239D812yes—
57C23×C239C2×D411yescharacteristic
58C2×C4×C239—21no—
59C2×C4×C239—41no—
60C2×C4×C239—41no—
61C2×C4×C239—41no—
62C2×C4×C239—41no—
63C2×C4×C239—41no—
64C2×C4×C239—41no—
65C2×C4×C239—41no—
66C2×C4×C239—41no—
67C2×C4×C239C2×D412yes—
68C22×C239—21no—
69C22×C239—21no—
70C22×C239—22no—
71C22×C239—42no—
72C22×C239—41no—
73C22×C239—41no—
74C22×C239—81no—
75C22×C239#12011yescharacteristic
76C22×C239C2×D811yescharacteristic
77C22×C239AGL(1,ℤ/8)11yescharacteristic
78C2×D239—42no—
79C2×D239—42no—
80C2×D239—42no—
81C2×D239—84no—
82C4×C239—22no—
83C4×C239—41no—
84C4×C239—81no—
85C4×C239—81no—
86Dic239—42no—
87C2×C239—21no—
88C2×C239—21no—
89C2×C239—42no—
90C2×C239#44711yescharacteristic
91C2×C239#45511yescharacteristic
92C2×C239#45811yescharacteristic
93D239—82no—
94C239#160711yescharacteristic, complemented, Sylow
95#1607—2391nomaximal, Sylow
96#534—2391no—
97#480—2392no—
98#397D23911yescharacteristic, complemented
99#327—2392no—
100#323—2391no—
101C22×D4—4781no—
102#123—4782no—
103#121—4781no—
104#121—2392no—
105#120—4782no—
106C2×C4⋊C4C2×D23911yescharacteristic, complemented
107C2×C22⋊C4—21no—
108C2×C22⋊C4C2×D23911yescharacteristic
109#107—4782no—
110#102—4782no—
111C22⋊C8—2392no—
112#95—21no—
113#95C2×D23911yescharacteristic, complemented
114C24—4781no—
115C24C22⋊D23911yescharacteristic
116C2×D4—9562no—
117C2×D4—9562no—
118C2×D4—4781no—
119C2×D4—4782no—
120C2×D4—4782no—
121C2×D4—2392no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—4781no—
125C22×C4C22⋊D23911yescharacteristic
126C22×C4C22×D23911yescharacteristic
127C2×C8—4782no—
128C4⋊C4—22no—
129C4⋊C4—4781no—
130C4⋊C4—2392no—
131C22⋊C4—22no—
132C22⋊C4—42no—
133C22⋊C4—4782no—
134C22⋊C4—4782no—
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23—19121no—
140C23—19121no—
141C23—9562no—
142C23—4782no—
143C23#1683853312yes—
144C23C2×C22⋊D23911yescharacteristic
145D4—19121no—
146D4—9562no—
147D4—9564no—
148D4—9562no—
149D4—9562no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—9562no—
160C2×C4—4782no—
161C2×C4D4×D23912yes—
162C8—9562no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—81no—
170C22—19124no—
171C22—9562no—
172C22—9562no—
173C22—9562no—
174C22#2143992811yescharacteristic
175C22C2×#1683853311yescharacteristic
176C22#2143998511yescharacteristic
177C4—22no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—9562no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—19122no—
186C2#2950490511yescharacteristic
187C2#2950494911yescharacteristic
188C2#2950496111yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC22×C4×C239C23
FrattiniC22×C4C22×D239
Fitting#397×C239C2
socleC22×C239#120
prime radical#29505334C2
hypercenter#397D239
hypocenterC239#1607
LCSG ▷ C22×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #29505085C2semidirect
3. #29504505C2semidirect
4. #29504496C2semidirect
5. #397×C239C2semidirect
13. C22⋊(C239⋊C8)C22semidirect
14. C2×C4⋊C4×C239C22semidirect
18. #95×C239C22semidirect
94. C239#1607semidirect
98. #397D239semidirect
106. C2×C4⋊C4C2×D239semidirect
113. #95C2×D239semidirect

Maximal subgroups

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

subgroupindex
#295053342
#295050852
#295045052
#295044962
#397×C2392
#1607239