Finite Group Databasebeta

← #49121781

Subgroups — #49121781

Order 36224.

312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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#31827232C211yesmaximal, characteristic
2#31827036C211yesmaximal, characteristic
3#31826473C212yesmaximal, complemented
4#31826221C212yesmaximal, complemented
5#410×C283C211yesmaximal, characteristic
6C22×Dic566C2211yescharacteristic
7#22583617—24no—
8C2×#17985376—22no—
9C2×#17985376C2212yes—
10#22583608C412yescomplemented
11#22583597C412yescomplemented
12#22583591—22no—
13#22583589—22no—
14#22583569C2211yescharacteristic
15#22583533—24no—
16C2×#41×C283C2211yescharacteristic
17#117×C283C2212yes—
18#99×C283—22no—
19C2×Dic566—21no—
20C2×Dic566—22no—
21C2×Dic566—22no—
22C2×Dic566C2×C412yes—
23C22×Dic283—21no—
24#17985376—24no—
25#17985376—22no—
26#17985376—22no—
27C2×C283⋊C8—24no—
28C2×C283⋊C8D414yes—
29C4⋊Dic283—21no—
30Dic283⋊C4—24no—
31C22⋊Dic283—24no—
32C22⋊Dic283—21no—
33C4×Dic283C2×C412yes—
34#41×C283—22no—
35#41×C283—22no—
36C2×Q8×C283C2×C411yescharacteristic
37C2×D4×C283C2×C411yescharacteristic
38C2×D4×C283D412yes—
39C22×C4×C283D412yes—
40C22×C4×C283C2311yescharacteristic
41C4⋊C4×C283—22no—
42C22⋊C4×C283—22no—
43C42×C283—22no—
44Dic566—24no—
45Dic566—41no—
46Dic566—41no—
47C2×Dic283—22no—
48C2×Dic283—22no—
49C2×Dic283—42no—
50C283⋊C8—24no—
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×C283—42no—
59C2×C4×C283C22⋊C412yes—
60C2×C4×C283C22×C411yescharacteristic
61C2×C4×C283C2×D412yes—
62C2×C4×C283C2×D411yescharacteristic
63C2×C4×C283#4112yes—
64C22×C283—22no—
65C22×C283—41no—
66C22×C283—42no—
67C22×C283C2×C22⋊C411yescharacteristic
68C22×C283#12112yes—
69C4×C283—22no—
70C4×C283—82no—
71C4×C283C4×D412yes—
72C4×C283#12011yescharacteristic
73C4×C283#12311yescharacteristic
74Dic283—42no—
75Dic283—42no—
76C2×C283—21no—
77C2×C283—22no—
78C2×C283—42no—
79C2×C283#38611yescharacteristic
80C283#190911yescharacteristic, complemented, Sylow
81#1909—2831nomaximal, Sylow
82#568—2831no—
83#536—2831no—
84#419—2832no—
85#410D28311yescharacteristic
86H(3,ℤ/4)—2832no—
87C2×#41C2×D28311yescharacteristic
88C22×Q8—2831no—
89#131—5664no—
90C2×M16—2832no—
91C2×M16—5662no—
92C4⋊Q8—2832no—
93#124—2832no—
94#123—5662no—
95C22⋊Q8—5662no—
96#117—2831no—
97#117C2×D28312yes—
98#103—5664no—
99#99—22no—
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×D4C22⋊D28312yes—
109C22×C4—5661no—
110C22×C4D113212yes—
111C22×C4C22×D28311yescharacteristic
112M16—5664no—
113M16—5662no—
114M16—5662no—
115C2×C8—2834no—
116C2×C8—5664no—
117C4⋊C4—22no—
118C4⋊C4—5664no—
119C4⋊C4—5661no—
120C22⋊C4—22no—
121C22⋊C4—5664no—
122C22⋊C4—5661no—
123C42—22no—
124C42—2832no—
125C23(C2×D283)⋊C412yes—
126C23C2×C22⋊D28311yescharacteristic
127Q8—22no—
128Q8—5664no—
129Q8—11321no—
130Q8—11321no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—5662no—
137C2×C4—5662no—
138C2×C4—11322no—
139C2×C4(C2×D283)⋊C412yes—
140C2×C4C2×C4×D28311yescharacteristic
141C2×C4D4×D28312yes—
142C2×C4C2×D113211yescharacteristic
143C2×C4#1798539112yes—
144C8—5664no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D283)⋊C411yescharacteristic
149C22#2258358212yes—
150C4—22no—
151C4—82no—
152C4—11322no—
153C4—11322no—
154C4(C22⋊D283)⋊C412yes—
155C4#2258358011yescharacteristic
156C4#2258359411yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#3182634211yescharacteristic
subgroupG/H
centerC2#31826342
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#410×C283C2
socleC2×C283#386
prime radicalC2×#41×C283C22
cosocleC22×C4×C283C23
hypercenter#410D283
hypocenterC283#1909
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #31826473C2semidirect
4. #31826221C2semidirect
10. #22583608C4semidirect
11. #22583597C4semidirect
80. C283#1909semidirect

Maximal subgroups

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

subgroupindex
#318272322
#318270362
#318264732
#318262212
#410×C2832
#1909283