Finite Group Databasebeta

← #49121783

Subgroups — #49121783

Order 36224.

312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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#31827036C211yesmaximal, characteristic
2#31826475C212yesmaximal, complemented
3#31826439C211yesmaximal, characteristic
4#31826222C212yesmaximal, complemented
5#568×C283C211yesmaximal, characteristic
6C22×Dic566C2211yescharacteristic
7#22583608C412yescomplemented
8#22583597C412yescomplemented
9#22583591—22no—
10#22583589—22no—
11#22583569C2212yes—
12#22583569C2211yescharacteristic
13#22583535—24no—
14#22583525—22no—
15C2×#41×C283C2211yescharacteristic
16#131×C283—24no—
17C2×M16×C283—22no—
18C2×M16×C283C2212yes—
19C2×Dic566—21no—
20C2×Dic566—22no—
21C2×Dic566—22no—
22C2×Dic566C2×C412yes—
23C22×Dic283—21no—
24C4⋊Dic283—21no—
25C4⋊Dic283—22no—
26Dic283⋊C4—24no—
27C22⋊Dic283—24no—
28C22⋊Dic283—21no—
29C22⋊Dic283—22no—
30C4×Dic283—22no—
31C4×Dic283C2×C412yes—
32#41×C283—22no—
33#41×C283—22no—
34C2×Q8×C283C2×C411yescharacteristic
35C2×D4×C283C2×C411yescharacteristic
36C2×D4×C283D412yes—
37C22×C4×C283D412yes—
38C22×C4×C283C2311yescharacteristic
39M16×C283—24no—
40M16×C283—22no—
41M16×C283—22no—
42C2×C8×C283—24no—
43C2×C8×C283D414yes—
44Dic566—24no—
45Dic566—41no—
46Dic566—41no—
47C2×Dic283—22no—
48C2×Dic283—22no—
49C2×Dic283—42no—
50C2×Dic283—42no—
51C23×C283C22⋊C412yes—
52C23×C283C2×D411yescharacteristic
53Q8×C283—22no—
54D4×C283—24no—
55D4×C283—22no—
56C2×C4×C283—22no—
57C2×C4×C283—22no—
58C2×C4×C283C22⋊C412yes—
59C2×C4×C283C22×C411yescharacteristic
60C2×C4×C283C2×D412yes—
61C2×C4×C283C2×D411yescharacteristic
62C2×C4×C283#4112yes—
63C8×C283—24no—
64C22×C283—22no—
65C22×C283—41no—
66C22×C283—42no—
67C22×C283C2×C22⋊C411yescharacteristic
68C22×C283#12112yes—
69C4×C283—22no—
70C4×C283C4×D412yes—
71C4×C283#12011yescharacteristic
72C4×C283#12311yescharacteristic
73Dic283—42no—
74Dic283—42no—
75Dic283—82no—
76C2×C283—21no—
77C2×C283—22no—
78C2×C283—42no—
79C2×C283#38611yescharacteristic
80C283#190911yescharacteristic, complemented, Sylow
81#1909—2831nomaximal, Sylow
82#568D28311yescharacteristic
83#536—2831no—
84#419—2832no—
85#410—2831no—
86H(3,ℤ/4)—2832no—
87C2×#41C2×D28311yescharacteristic
88C22×Q8—2831no—
89#131—24no—
90C2×M16—22no—
91C2×M16C2×D28312yes—
92C4⋊Q8—2832no—
93#124—2832no—
94#123—5662no—
95C22⋊Q8—5662no—
96#117—2831no—
97#117—2832no—
98#103—5664no—
99#99—5662no—
100#41—22no—
101#41—22no—
102C2×Q8—2832no—
103C2×Q8—5661no—
104C2×Q8—5662no—
105C2×Q8—5662no—
106C2×Q8C4×D28311yescharacteristic
107C2×D4C4×D28311yescharacteristic
108C2×D4D113212yes—
109C22×C4—5661no—
110C22×C4C22⋊D28312yes—
111C22×C4C22×D28311yescharacteristic
112M16—24no—
113M16—22no—
114M16—22no—
115C2×C8—24no—
116C2×C8C22⋊D28314yes—
117C4⋊C4—5664no—
118C4⋊C4—5661no—
119C4⋊C4—5662no—
120C22⋊C4—5664no—
121C22⋊C4—5661no—
122C22⋊C4—5662no—
123C42—2832no—
124C42—5662no—
125C23(C2×D283)⋊C412yes—
126C23C2×D113211yescharacteristic
127Q8—22no—
128Q8—5664no—
129Q8—11321no—
130Q8—11321no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—5662no—
136C2×C4—5662no—
137C2×C4—11322no—
138C2×C4—11322no—
139C2×C4(C2×D283)⋊C412yes—
140C2×C4C2×C4×D28311yescharacteristic
141C2×C4C2×C22⋊D28312yes—
142C2×C4C2×C22⋊D28311yescharacteristic
143C2×C4#1798539212yes—
144C8—24no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D283)⋊C411yescharacteristic
149C22#2258358412yes—
150C4—22no—
151C4—11322no—
152C4—11322no—
153C4—22642no—
154C4C4×C22⋊D28312yes—
155C4#2258357911yescharacteristic
156C4#2258359311yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#3182634411yescharacteristic
subgroupG/H
centerC2#31826344
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#568×C283C2
socleC2×C283#386
prime radicalC2×#41×C283C22
cosocleC22×C4×C283C23
hypercenter#568D283
hypocenterC283#1909
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #31826475C2semidirect
4. #31826222C2semidirect
7. #22583608C4semidirect
8. #22583597C4semidirect
80. C283#1909semidirect

Maximal subgroups

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

subgroupindex
#318270362
#318264752
#318264392
#318262222
#568×C2832
#1909283