Finite Group Databasebeta

← #44484650

Subgroups — #44484650

Order 30592.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#29505240C211yesmaximal, characteristic
2#29504754C211yesmaximal, characteristic
3#29504745C211yesmaximal, characteristic
4#29504533C211yesmaximal, characteristic, complemented
5#29504531C211yesmaximal, characteristic, complemented
6#29504528C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C239C211yesmaximal, characteristic, complemented
8C2×#16838548C2211yescharacteristic
9C2×#16838532C2211yescharacteristic
10#21439925—21no—
11#21439922—21no—
12(C22⋊D239)⋊C4—22no—
13#21439919C2211yescharacteristic
14#21439917C412yescomplemented
15C2×C4×Dic239C2211yescharacteristic
16C42×D239C412yescomplemented
17#21439878—21no—
18#21439876—21no—
19#21439874—22no—
20C2×M16×C239C2211yescharacteristic
21#117×C239C2211yescharacteristic
22#117×C239C2211yescharacteristic
23#16838548—21no—
24#16838548—21no—
25#16838548—21no—
26#16838548—21no—
27C2×Dic478D411yescharacteristic
28C2×D956D411yescharacteristic
29C2×C22⋊D239D412yes—
30C22×Dic239—21no—
31C2×C4×D239—22no—
32C2×C4×D239C2×C412yes—
33#16838532—21no—
34#16838532—21no—
35C2×C239⋊C8—21no—
36C4⋊Dic239—21no—
37Dic239⋊C4—22no—
38C22⋊Dic239—21no—
39(C2×D239)⋊C4—22no—
40C4×Dic239—22no—
41C4×Dic239—21no—
42C4×Dic239—21no—
43C4×Dic239C2×C411yescharacteristic
44C4×Dic239C2×C411yescharacteristic
45C22×C4×C239C2311yescharacteristic
46M16×C239—21no—
47M16×C239—21no—
48C2×C8×C239—21no—
49C4⋊C4×C239—21no—
50C4⋊C4×C239—21no—
51C22⋊C4×C239—21no—
52C22⋊C4×C239—21no—
53C42×C239—21no—
54C42×C239C2×C412yes—
55C22×D239C22⋊C412yes—
56Dic478—21no—
57Dic478—21no—
58D956—21no—
59D956—21no—
60C22⋊D239—22no—
61C22⋊D239—22no—
62C2×Dic239—21no—
63C2×Dic239—21no—
64C2×Dic239—42no—
65C2×Dic239—41no—
66C2×Dic239C22⋊C412yes—
67C4×D239—22no—
68C4×D239—22no—
69C4×D239—44no—
70C239⋊C8—41no—
71C23×C239C2×D411yescharacteristic
72C2×C4×C239—22no—
73C2×C4×C239—41no—
74C2×C4×C239C22×C411yescharacteristic
75C2×C4×C239C2×D411yescharacteristic
76C2×C4×C239#4111yescharacteristic
77C2×C4×C239#4111yescharacteristic
78C2×C4×C239#4111yescharacteristic
79C2×C4×C239#4111yescharacteristic
80C8×C239—41no—
81C22×C239—41no—
82C22×C239C2×C22⋊C411yescharacteristic
83C22×C239#12311yescharacteristic
84C22×C239#12311yescharacteristic
85C2×D239—22no—
86C2×D239—42no—
87C4×C239—42no—
88C4×C239—81no—
89C4×C239#11711yescharacteristic
90C4×C239#11711yescharacteristic
91C4×C239#12311yescharacteristic
92C4×C239#12311yescharacteristic
93Dic239—22no—
94Dic239—22no—
95Dic239—41no—
96Dic239—81no—
97C2×C239—21no—
98C2×C239—21no—
99C2×C239—21no—
100C2×C239#38111yescharacteristic
101D239—42no—
102C239#182711yescharacteristic, complemented, Sylow
103#1827—2391nomaximal, Sylow
104C4×#41—2391no—
105#413—2391no—
106#410—2391no—
107#339—2391no—
108#339—2391no—
109H(3,ℤ/4)—2391no—
110H(3,ℤ/4)D23911yescharacteristic, complemented
111C2×#41—2391no—
112C2×M16—2391no—
113C2×M16C2×D23911yescharacteristic
114C4×Q8—4781no—
115C4×D4—4782no—
116C4×D4—4781no—
117#117—2391no—
118#117—2392no—
119#117C2×D23911yescharacteristic
120#117C2×D23911yescharacteristic
121C2×C42—2391no—
122C2×C42—2392no—
123#101—4781no—
124#100—4781no—
125#99—4782no—
126#41—4781no—
127#41—4781no—
128#41—4781no—
129#41—4781no—
130C2×Q8—2391no—
131C2×D4—2392no—
132C2×D4—2391no—
133C22×C4—4782no—
134C22×C4—4781no—
135C22×C4—2392no—
136C22×C4C22×D23911yescharacteristic
137M16—21no—
138M16—21no—
139M16—4781no—
140M16—4781no—
141C2×C8—21no—
142C2×C8—4781no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—4782no—
146C4⋊C4—4781no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—4782no—
150C22⋊C4—4781no—
151C42—21no—
152C42—4782no—
153C42—4781no—
154C42—4781no—
155C42—2391no—
156C42—2391no—
157C42C4×D23912yes—
158C23—2392no—
159C23D4×D23911yescharacteristic
160Q8—4781no—
161Q8—4781no—
162D4—4782no—
163D4—4782no—
164D4—4781no—
165D4—4781no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—9564no—
169C2×C4—9561no—
170C2×C4—9562no—
171C2×C4—4781no—
172C2×C4—4781no—
173C2×C4—4782no—
174C2×C4—4782no—
175C2×C4—2392no—
176C2×C4C2×C4×D23911yescharacteristic
177C2×C4D4×D23911yescharacteristic
178C2×C4#1683854711yescharacteristic
179C2×C4#1683854811yescharacteristic
180C2×C4#1683854811yescharacteristic
181C2×C4#1683854911yescharacteristic
182C8—41no—
183C8—9561no—
184C22—41no—
185C22—9562no—
186C22—4782no—
187C22C22⋊C4×D23911yescharacteristic
188C22#2143994211yescharacteristic
189C22#2143994511yescharacteristic
190C4—42no—
191C4—81no—
192C4—19121no—
193C4—9561no—
194C4—4782no—
195C4—4782no—
196C4#2143991711yescharacteristic
197C4#2143991811yescharacteristic
198C4#2143994211yescharacteristic
199C4#2143994511yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—9562no—
204C2#2950463411yescharacteristic
subgroupG/H
centerC4#21439917
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
FittingH(3,ℤ/4)×C239C2
socleC2×C239#381
prime radicalC2×#16838548C22
cosocleC22×C4×C239C23
hypercenterH(3,ℤ/4)D239
hypocenterC239#1827
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #29504533C2semidirect
5. #29504531C2semidirect
6. #29504528C2semidirect
7. H(3,ℤ/4)×C239C2semidirect
14. #21439917C4semidirect
16. C42×D239C4semidirect
102. C239#1827semidirect
110. H(3,ℤ/4)D239semidirect

Maximal subgroups

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

subgroupindex
#295052402
#295047542
#295047452
#295045332
#295045312
#295045282
H(3,ℤ/4)×C2392
#1827239