Finite Group Databasebeta

← #49121362

Subgroups — #49121362

Order 36224.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic283C211yesmaximal, characteristic
2#31826449C211yesmaximal, characteristic
3#31826224C212yesmaximal, complemented
4#31826221C212yesmaximal, complemented
5#410×C283C211yesmaximal, characteristic
6C2×#17985376C2212yes—
7Q8×Dic283—21no—
8D4×Dic283—22no—
9D4×Dic283—21no—
10#22583569C412yescomplemented
11#22583569C2211yescharacteristic
12C2×C4×Dic283C412yescomplemented
13C2×C4×Dic283C2211yescharacteristic
14#22583529—21no—
15#22583527—21no—
16C2×#41×C283C2211yescharacteristic
17#117×C283C2212yes—
18#99×C283—22no—
19C22×Dic283—22no—
20C22×Dic283—21no—
21#17985376—22no—
22#17985376—22no—
23C2×C283⋊C8—22no—
24C4⋊Dic283—22no—
25C4⋊Dic283—21no—
26C22⋊Dic283—22no—
27C22⋊Dic283—21no—
28C4×Dic283—22no—
29C4×Dic283—21no—
30C4×Dic283C2×C411yescharacteristic
31C4×Dic283C2×C412yes—
32C4×Dic283C2×C411yescharacteristic
33#41×C283—22no—
34#41×C283—22no—
35C2×Q8×C283D411yescharacteristic
36C2×D4×C283D412yes—
37C2×D4×C283D411yescharacteristic
38C22×C4×C283C2×C412yes—
39C22×C4×C283C2311yescharacteristic
40C4⋊C4×C283—22no—
41C22⋊C4×C283—22no—
42C42×C283—22no—
43C2×Dic283—21no—
44C2×Dic283—22no—
45C2×Dic283—21no—
46C2×Dic283—42no—
47C2×Dic283—44no—
48C283⋊C8—42no—
49C23×C283C22⋊C412yes—
50C23×C283C2×D411yescharacteristic
51Q8×C283—22no—
52D4×C283—24no—
53D4×C283—22no—
54C2×C4×C283—22no—
55C2×C4×C283—22no—
56C2×C4×C283—42no—
57C2×C4×C283C22⋊C412yes—
58C2×C4×C283C22×C411yescharacteristic
59C2×C4×C283C2×D411yescharacteristic
60C2×C4×C283#4112yes—
61C2×C4×C283#4112yes—
62C22×C283—22no—
63C22×C283—41no—
64C22×C283—42no—
65C22×C283C2×C22⋊C411yescharacteristic
66C22×C283#12312yes—
67C4×C283—22no—
68C4×C283—82no—
69C4×C283#11711yescharacteristic
70C4×C283#11711yescharacteristic
71C4×C283#12312yes—
72Dic283—22no—
73Dic283—42no—
74Dic283—41no—
75C2×C283—21no—
76C2×C283—22no—
77C2×C283—42no—
78C2×C283#38111yescharacteristic
79C283#182711yescharacteristic, complemented, Sylow
80#1827—2831nomaximal, Sylow
81C4×#41—2831no—
82#413—2831no—
83#410D28311yescharacteristic
84#339—2832no—
85H(3,ℤ/4)—2832no—
86C2×#41C2×D28311yescharacteristic
87C2×M16—2832no—
88C4×Q8—5661no—
89C4×D4—5662no—
90C4×D4—5661no—
91#117—2832no—
92#117—2831no—
93#117C2×D28312yes—
94C2×C42—2832no—
95C2×C42—2831no—
96#101—5661no—
97#100—5661no—
98#99—22no—
99#41—22no—
100#41—22no—
101C2×Q8D113211yescharacteristic
102C2×D4C22⋊D28312yes—
103C2×D4D113211yescharacteristic
104C22×C4—5662no—
105C22×C4—5661no—
106C22×C4C4×D28312yes—
107C22×C4C22×D28311yescharacteristic
108M16—5662no—
109M16—5662no—
110C2×C8—5662no—
111C4⋊C4—22no—
112C4⋊C4—5662no—
113C4⋊C4—5661no—
114C22⋊C4—22no—
115C22⋊C4—5662no—
116C22⋊C4—5661no—
117C42—22no—
118C42—2831no—
119C42—2832no—
120C42—2831no—
121C42—5662no—
122C42—5661no—
123C23(C2×D283)⋊C412yes—
124C23C2×C22⋊D28311yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—5661no—
132C2×C4—5662no—
133C2×C4—5661no—
134C2×C4—11322no—
135C2×C4—11324no—
136C2×C4(C2×D283)⋊C412yes—
137C2×C4C2×C4×D28311yescharacteristic
138C2×C4C2×D113211yescharacteristic
139C2×C4#1798539112yes—
140C2×C4#1798539112yes—
141C8—11322no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×(C2×D283)⋊C411yescharacteristic
146C22#2258359112yes—
147C4—22no—
148C4—82no—
149C4—5662no—
150C4—11322no—
151C4—11321no—
152C4#2258356611yescharacteristic
153C4#2258356611yescharacteristic
154C4#2258359412yes—
155C2—22no—
156C2—21no—
157C2—42no—
158C2#3182632611yescharacteristic
subgroupG/H
centerC4#22583566
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#410×C283C2
socleC2×C283#381
prime radicalC2×#41×C283C22
cosocleC22×C4×C283C23
hypercenter#410D283
hypocenterC283#1827
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #31826224C2semidirect
4. #31826221C2semidirect
10. #22583569C4semidirect
12. C2×C4×Dic283C4semidirect
79. C283#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic2832
#318264492
#318262242
#318262212
#410×C2832
#1827283