Finite Group Databasebeta

← #44507992

Subgroups — #44507992

Order 30848.

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

normal subgroups only

This group has 340 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#29508281C211yesmaximal, characteristic
2#29507701C211yesmaximal, characteristic, complemented
3C2×#21440558C212yesmaximal, complemented
4#29507489C212yesmaximal, complemented
5#568×C241C211yesmaximal, characteristic, complemented
6C22×D964C2211yescharacteristic
7C2×#16838754C2212yes—
8#21440638—21no—
9#21440631—21no—
10#21440616—22no—
11#21440610C414yes—
12#21440601C2211yescharacteristic
13#21440561—21no—
14#21440559—21no—
15#21440558—24no—
16C2×#41×C241C2211yescharacteristic
17#131×C241—24no—
18C2×M16×C241—22no—
19C2×M16×C241C2212yes—
20C23×D241C2×C412yes—
21C2×D964—22no—
22C2×D964—21no—
23C2×D964—21no—
24C2×D964—22no—
25C2×C22⋊D241—24no—
26#16838754—22no—
27#16838754—22no—
28C2×#14515349—22no—
29C4⋊Dic241—21no—
30C22⋊Dic241C2×C412yes—
31#16838747—24no—
32C4×Dic241—21no—
33#41×C241—22no—
34#41×C241—22no—
35C2×Q8×C241D411yescharacteristic
36C2×D4×C241C2×C412yes—
37C2×D4×C241D411yescharacteristic
38C22×C4×C241D412yes—
39C22×C4×C241C2311yescharacteristic
40M16×C241—24no—
41M16×C241—22no—
42M16×C241D414yescomplemented
43C2×C8×C241—24no—
44C2×C8×C241—22no—
45C22×D241—22no—
46C22×D241—24no—
47C22×D241—82no—
48D964—41no—
49D964—42no—
50D964—41no—
51C22⋊D241—84no—
52C2×Dic241—22no—
53#14515349—42no—
54C23×C241C22⋊C412yes—
55C23×C241C22×C411yescharacteristic
56Q8×C241—22no—
57D4×C241—24no—
58D4×C241—22no—
59C2×C4×C241—22no—
60C2×C4×C241—22no—
61C2×C4×C241C22⋊C412yes—
62C2×C4×C241C2×D412yes—
63C2×C4×C241C2×D411yescharacteristic
64C2×C4×C241C2×D411yescharacteristic
65C2×C4×C241#4112yes—
66C8×C241—24no—
67C22×C241—22no—
68C22×C241—41no—
69C22×C241—42no—
70C22×C241C2×C22⋊C411yescharacteristic
71C22×C241C4×D412yes—
72C2×D241—44no—
73C2×D241—42no—
74C2×D241—84no—
75C4×C241—22no—
76C4×C241#12011yescharacteristic
77C4×C241#12112yes—
78C4×C241#12311yescharacteristic
79Dic241—42no—
80C2×C241—21no—
81C2×C241—22no—
82C2×C241—42no—
83C2×C241#38611yescharacteristic
84D241—82no—
85C241#191411yescharacteristic, complemented, Sylow
86#1914—2411nomaximal, Sylow
87#568D24111yescharacteristic, complemented
88#535—2411no—
89#413—2411no—
90C2×#100—2412no—
91#344—2412no—
92C2×#41C2×D24111yescharacteristic
93C22×D4—2411no—
94#131—24no—
95C2×M16—22no—
96C2×M16—2412no—
97C2×M16C2×D24112yes—
98#127—4821no—
99#124—4821no—
100#121—4822no—
101#120—2414no—
102#117—2411no—
103#101—4821no—
104#100—4821no—
105#100—4824no—
106C24—2412no—
107#41—22no—
108#41—22no—
109C2×Q8D96411yescharacteristic
110C2×D4—4824no—
111C2×D4—4822no—
112C2×D4—4821no—
113C2×D4—4821no—
114C2×D4—4822no—
115C2×D4C4×D24112yes—
116C2×D4D96411yescharacteristic
117C22×C4C22⋊D24112yes—
118C22×C4C22×D24111yescharacteristic
119M16—24no—
120M16—22no—
121M16—4822no—
122M16—4822no—
123M16C22⋊D24114yescomplemented
124C2×C8—24no—
125C2×C8—22no—
126C2×C8—4822no—
127C4⋊C4—4821no—
128C22⋊C4—4824no—
129C22⋊C4—2412no—
130C42—4821no—
131C23—19282no—
132C23—4824no—
133C23—4822no—
134C23#1683874712yes—
135C23C2×C4×D24111yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—19284no—
140D4—9641no—
141D4—9642no—
142D4—9641no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—4822no—
146C2×C4#1683874712yes—
147C2×C4C2×C22⋊D24112yes—
148C2×C4C2×C22⋊D24111yescharacteristic
149C2×C4C2×D96411yescharacteristic
150C2×C4#1683877012yes—
151C8—24no—
152C8—9642no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—19284no—
157C22—9644no—
158C22—9642no—
159C22C2×#1683874711yescharacteristic
160C22C4×C22⋊D24112yes—
161C4—22no—
162C4—9642no—
163C4#2144061111yescharacteristic
164C4#2144061612yes—
165C4#2144062511yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—19282no—
170C2#2950759611yescharacteristic
subgroupG/H
centerC2#29507596
commutatorC23×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#568×C241C2
socleC2×C241#386
prime radical#29508281C2
cosocleC22×C4×C241C23
hypercenter#568D241
hypocenterC241#1914
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #29507701C2semidirect
3. C2×#21440558C2semidirect
4. #29507489C2semidirect
5. #568×C241C2semidirect
42. M16×C241D4semidirect
85. C241#1914semidirect
87. #568D241semidirect
123. M16C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295082812
#295077012
C2×#214405582
#295074892
#568×C2412
#1914241