Finite Group Databasebeta

← #44485450

Subgroups — #44485450

Order 30592.

296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×#16838535C211yesmaximal, characteristic
2C2×#21439895C211yesmaximal, characteristic, complemented
3#29504776C211yesmaximal, characteristic
4C2×#21439879C211yesmaximal, characteristic, complemented
5C2×#21439876C211yesmaximal, characteristic
6#29504728C211yesmaximal, characteristic, complemented
7#419×C239C211yesmaximal, characteristic, complemented
8C22×D956C2211yescharacteristic
9C2×#16838535—21no—
10C2×#16838535—21no—
11C2×#16838535—22no—
12C2×#16838535C414yescomplemented
13C2×#16838532C2211yescharacteristic
14C2×#16838532C2211yescharacteristic
15C22×C239⋊C8C2211yescharacteristic
16#21439895—22no—
17#21439880—22no—
18#21439879—22no—
19#21439876—22no—
20#21439871—21no—
21C4×C239⋊C8—21no—
22C22×Q8×C239C2211yescharacteristic
23C2×M16×C239C2211yescharacteristic
24#117×C239C2211yescharacteristic
25#103×C239—22no—
26C23×D239—21no—
27C2×D956—21no—
28C2×D956—21no—
29C2×D956—21no—
30C2×D956—21no—
31C2×D956—21no—
32C2×D956C2×C412yes—
33#16838535—24no—
34#16838535—24no—
35#16838532—21no—
36#16838532—21no—
37#16838532—21no—
38#16838532D412yes—
39C2×C239⋊C8—21no—
40C2×C239⋊C8—21no—
41C2×C239⋊C8C2×C412yes—
42C2×C239⋊C8D411yescharacteristic
43C2×C239⋊C8D411yescharacteristic
44C2×C239⋊C8D412yes—
45C2×Q8×C239—21no—
46C2×Q8×C239—21no—
47C2×Q8×C239—21no—
48C2×Q8×C239—21no—
49C2×Q8×C239—21no—
50C2×Q8×C239C2×C412yes—
51C22×C4×C239—21no—
52C22×C4×C239C2311yescharacteristic
53M16×C239—21no—
54M16×C239—21no—
55C2×C8×C239—21no—
56C4⋊C4×C239D412yes—
57C22⋊C4×C239—21no—
58C42×C239—21no—
59C22×D239—22no—
60C22×D239—41no—
61C22×D239—41no—
62C22×D239—82no—
63D956—22no—
64D956—22no—
65D956—41no—
66D956—41no—
67C239⋊C8—22no—
68C239⋊C8—41no—
69C239⋊C8C22⋊C412yes—
70C239⋊C8C22⋊C412yes—
71C23×C239#4111yescharacteristic
72Q8×C239—22no—
73Q8×C239—22no—
74Q8×C239—41no—
75Q8×C239—41no—
76C2×C4×C239—22no—
77C2×C4×C239—22no—
78C2×C4×C239—41no—
79C2×C4×C239—41no—
80C2×C4×C239C22×C411yescharacteristic
81C2×C4×C239C2×D411yescharacteristic
82C2×C4×C239C2×D411yescharacteristic
83C2×C4×C239C2×D411yescharacteristic
84C2×C4×C239C2×D411yescharacteristic
85C2×C4×C239#4111yescharacteristic
86C8×C239—41no—
87C22×C239—22no—
88C22×C239C4×D411yescharacteristic
89C22×C239#12111yescharacteristic
90C22×C239#12411yescharacteristic
91C2×D239—42no—
92C2×D239—82no—
93C2×D239—82no—
94C2×D239—82no—
95C4×C239—42no—
96C4×C239—42no—
97C4×C239C2×C22⋊C411yescharacteristic
98C4×C239C4×D411yescharacteristic
99C4×C239#12111yescharacteristic
100C4×C239#12711yescharacteristic
101C2×C239—21no—
102C2×C239—21no—
103C2×C239#39011yescharacteristic
104C2×C239#47112yes—
105D239—82no—
106C239#197711yescharacteristic, complemented, Sylow
107#1977—2391nomaximal, Sylow
108C22×SD16—2391no—
109C2×#108—2391no—
110#419D23911yescharacteristic, complemented
111#418—2391no—
112C2×#101—2391no—
113C2×#100—2391no—
114#405—2391no—
115C22×Q8C2×D23911yescharacteristic
116C22×D4—2391no—
117C2×SD16—4781no—
118C2×SD16—4781no—
119C2×SD16—4782no—
120C2×SD16—2394no—
121C2×M16—2391no—
122C2×M16—2391no—
123C2×M16C2×D23911yescharacteristic
124C22×C8—2391no—
125#117C2×D23911yescharacteristic
126#108—4782no—
127#103—22no—
128#102—4782no—
129#101—4782no—
130#100—4782no—
131#97—4781no—
132C4×C8—4781no—
133C24—4781no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8C4×D23912yes—
140C2×D4—4781no—
141C2×D4—4781no—
142C2×D4—4781no—
143C2×D4—4781no—
144C2×D4—4781no—
145C2×D4—2392no—
146C22×C4—21no—
147C22×C4C22×D23911yescharacteristic
148SD16—4784no—
149SD16—4784no—
150M16—21no—
151M16—21no—
152M16—4781no—
153M16—4781no—
154M16—4781no—
155M16—2392no—
156C2×C8—21no—
157C2×C8—4781no—
158C2×C8—4781no—
159C2×C8—2392no—
160C2×C8—2391no—
161C2×C8—2391no—
162C2×C8—2392no—
163C4⋊C4C22⋊D23912yes—
164C22⋊C4—21no—
165C42—21no—
166C23—19122no—
167C23—9561no—
168C23—9561no—
169C23—4782no—
170C23#1683854711yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175D4—9561no—
176D4—9561no—
177D4—4782no—
178D4—4782no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4C2×C4×D23911yescharacteristic
184C2×C4D4×D23911yescharacteristic
185C2×C4D4×D23911yescharacteristic
186C2×C4D4×D23911yescharacteristic
187C2×C4C2×C22⋊D23911yescharacteristic
188C2×C4#1683854811yescharacteristic
189C8—41no—
190C8—9561no—
191C8—4782no—
192C8—2392no—
193C8—2392no—
194C22—22no—
195C22—19122no—
196C22—19122no—
197C22—19122no—
198C22—9562no—
199C22(C22⋊D239)⋊C411yescharacteristic
200C22#2143993211yescharacteristic
201C22#2143994611yescharacteristic
202C4—42no—
203C4—42no—
204C4C22⋊C4×D23911yescharacteristic
205C4C4×C22⋊D23911yescharacteristic
206C4#2143993311yescharacteristic
207C4#2143995611yescharacteristic
208C2—21no—
209C2—21no—
210C2—19122no—
211C2#2950467211yescharacteristic
212C2#2950503712yes—
subgroupG/H
centerC22#21439932
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#419×C239C2
socleC22×C239#121
prime radicalC22×D956C22
cosocleC22×C4×C239C23
hypercenter#419D239
hypocenterC239#1977
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C2×#21439895C2semidirect
4. C2×#21439879C2semidirect
6. #29504728C2semidirect
7. #419×C239C2semidirect
12. C2×#16838535C4semidirect
106. C239#1977semidirect
110. #419D239semidirect

Maximal subgroups

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

subgroupindex
C22×#168385352
C2×#214398952
#295047762
C2×#214398792
C2×#214398762
#295047282
#419×C2392
#1977239