Finite Group Databasebeta

← #44483138

Subgroups — #44483138

Order 30592.

270 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 63 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#29505321C211yesmaximal, characteristic
2#29504724C212yesmaximal, complemented
3#29504512C211yesmaximal, characteristic, complemented
4#29504511C212yesmaximal, complemented
5#329×C239C211yesmaximal, characteristic, complemented
6C2×#16838549C411yescharacteristic
7C2×#16838547C411yescharacteristic
8C2×#16838531—22no—
9#21439958C411yescharacteristic
10#21439956C411yescharacteristic
11#21439948C2211yescharacteristic
12#21439933—22no—
13(C22⋊D239)⋊C4—22no—
14C42×D239C2211yescharacteristic
15#21439871C2212yes—
16C8×Dic239—22no—
17#124×C239C2211yescharacteristic
18#97×C239C2212yes—
19#16838549—42no—
20#16838547—42no—
21C2×Dic478C2×C411yescharacteristic
22C2×D956—21no—
23C2×D956C2×C411yescharacteristic
24C2×C22⋊D239—21no—
25C2×C22⋊D239—22no—
26C22×Dic239—21no—
27C2×C4×D239—21no—
28C2×C4×D239C2×C411yescharacteristic
29C2×C4×D239D412yes—
30#16838531—28no—
31C2×C239⋊C8—22no—
32Dic239⋊C4—22no—
33(C2×D239)⋊C4—22no—
34C4×Dic239C2×C411yescharacteristic
35C4×Dic239D412yes—
36C2×Q8×C239C2×C411yescharacteristic
37C2×D4×C239C2×C411yescharacteristic
38C2×C8×C239—22no—
39C22⋊C4×C239—22no—
40C42×C239C2311yescharacteristic
41C22×D239—21no—
42C22×D239C22⋊C411yescharacteristic
43Dic478—41no—
44D956—41no—
45D956—42no—
46C22⋊D239—42no—
47C22⋊D239—44no—
48C2×Dic239—21no—
49C2×Dic239—42no—
50C2×Dic239C22⋊C411yescharacteristic
51C2×Dic239C22⋊C412yes—
52C4×D239—22no—
53C4×D239—24no—
54C4×D239—42no—
55C239⋊C8—24no—
56C23×C239—21no—
57Q8×C239—41no—
58D4×C239—41no—
59C2×C4×C239—21no—
60C2×C4×C239C22×C411yescharacteristic
61C2×C4×C239C2×D412yes—
62C8×C239—24no—
63C22×C239—41no—
64C22×C239—42no—
65C22×C239C2×C22⋊C411yescharacteristic
66C2×D239—21no—
67C2×D239—22no—
68C2×D239—41no—
69C2×D239—42no—
70C4×C239—21no—
71C4×C239—22no—
72C4×C239—41no—
73Dic239—41no—
74Dic239#10012yes—
75Dic239#10414yes—
76C2×C239—81no—
77C2×C239C2×#10011yescharacteristic
78C2×C239C2×#10412yes—
79D239—41no—
80D239—81no—
81C239#152511yescharacteristic, complemented, Sylow
82#1525—2391nomaximal, Sylow
83#532—2391no—
84C4×M16—2392no—
85#329—2391no—
86#329—2392no—
87#329D23911yescharacteristic, complemented
88C2×#41—2391no—
89C2×#41—2391no—
90C2×M16—4782no—
91C4⋊Q8—2391no—
92#127—2391no—
93#124—2391no—
94#124C2×D23911yescharacteristic
95#121—4782no—
96C4×D4—4782no—
97C2×C42—2391no—
98#97—2392no—
99#97C2×D23912yes—
100C4×C8—4782no—
101#41—9562no—
102#41—9562no—
103C2×Q8—2391no—
104C2×Q8C4×D23911yescharacteristic
105C2×D4—4781no—
106C2×D4—4781no—
107C2×D4—4782no—
108C2×D4—2391no—
109C2×D4C4×D23911yescharacteristic
110C22×C4—4781no—
111C22×C4—4781no—
112C22×C4—2391no—
113C22×C4—2392no—
114M16—4788no—
115C2×C8—22no—
116C2×C8—4782no—
117C4⋊C4—4782no—
118C22⋊C4—22no—
119C22⋊C4—4782no—
120C42—2391no—
121C42—2392no—
122C42C22×D23911yescharacteristic
123C23—21no—
124C23—4781no—
125C23—2391no—
126Q8—41no—
127Q8—9561no—
128D4—41no—
129D4—9561no—
130D4—9562no—
131D4—9562no—
132D4—9564no—
133C2×C4—21no—
134C2×C4—9562no—
135C2×C4—9562no—
136C2×C4—4784no—
137C2×C4—4782no—
138C2×C4—4781no—
139C2×C4—2392no—
140C2×C4—2391no—
141C2×C4C2×C4×D23911yescharacteristic
142C2×C4D4×D23912yes—
143C8—24no—
144C8—4784no—
145C22—42no—
146C22—41no—
147C22—9562no—
148C22—9561no—
149C22—4782no—
150C22—4781no—
151C22C22⋊C4×D23911yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—9561no—
156C4—2394no—
157C4—2392no—
158C2—81no—
159C2—19121no—
160C2—9561no—
161C2#100×D23911yescharacteristic
162C2#104×D23912yes—
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
Fitting#329×C239C2
socleC22×C239C2×C22⋊C4
prime radical#29505321C2
cosocleC42×C239C23
hypercenter#329D239
hypocenterC239#1525
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #29504724C2semidirect
3. #29504512C2semidirect
4. #29504511C2semidirect
5. #329×C239C2semidirect
81. C239#1525semidirect
87. #329D239semidirect

Maximal subgroups

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

subgroupindex
#295053212
#295047242
#295045122
#295045112
#329×C2392
#1525239