Finite Group Databasebeta

← #44509463

Subgroups — #44509463

Order 30848.

248 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 41 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#29508459C211yesmaximal, characteristic, complemented
2#29507892C212yesmaximal, complemented
3#29507889C211yesmaximal, characteristic, complemented
4#29507513C212yesmaximal, complemented
5#355×C241C211yesmaximal, characteristic, complemented
6#21440690C2211yescharacteristic, complemented
7#21440670—22no—
8#21440668—21no—
9#21440631C2212yes—
10#21440630—21no—
11#21440628—22no—
12#21440612—22no—
13#21440610—21no—
14#21440570—21no—
15#21440568—22no—
16#21440561C2211yescharacteristic, complemented
17#124×C241C2211yescharacteristic
18#101×C241C2212yescomplemented
19C23×D241—21no—
20#16838771—41no—
21#16838770—22no—
22#16838770—21no—
23C2×Dic482—21no—
24Q8×D241—41no—
25C2×D964—21no—
26C2×D964D412yes—
27C2×C22⋊D241—22no—
28#16838759—42no—
29#16838758—41no—
30D1928—42no—
31#16838755—41no—
32#16838754—21no—
33C22⋊Dic241—21no—
34#16838747—22no—
35#16838747—22no—
36#16838747—22no—
37C4×Dic241D412yes—
38C2×Q8×C241C2311yescharacteristic
39C2×D4×C241D411yescharacteristic
40M16×C241—22no—
41C22⋊C4×C241—22no—
42C42×C241D411yescharacteristic
43C22×D241—22no—
44C22×D241—82no—
45C22×D241—81no—
46Dic482—21no—
47Dic482—22no—
48Dic482—81no—
49D964—21no—
50D964—22no—
51D964—42no—
52D964—81no—
53C22⋊D241—41no—
54C22⋊D241—82no—
55C2×Dic241—22no—
56C4×D241—42no—
57C4×D241—41no—
58#14515349—41no—
59C23×C241—21no—
60Q8×C241—41no—
61D4×C241—41no—
62C2×C4×C241—21no—
63C2×C4×C241C2×D412yes—
64C2×C4×C241C2×D411yescharacteristic
65C8×C241—42no—
66C22×C241—42no—
67C22×C241—41no—
68C22×C241#12011yescharacteristic
69C2×D241—42no—
70C2×D241—42no—
71C2×D241—41no—
72C2×D241—42no—
73C2×D241—84no—
74C4×C241—22no—
75C4×C241—21no—
76C4×C241—41no—
77Dic241—42no—
78Dic241—41no—
79C2×C241—21no—
80C2×C241—81no—
81C2×C241B(4,𝔽2)11yescharacteristic
82D241—81no—
83D241—82no—
84C241#220211yescharacteristic, complemented, Sylow
85#2202—2411nomaximal, Sylow
86H(3,𝔽4)—2411no—
87#454—2411no—
88#454—2412no—
89#355—2412no—
90#355D24111yescharacteristic, complemented
912−1+4—2411no—
92AGL(1,ℤ/8)—4822no—
93AGL(1,ℤ/8)—4821no—
94#124—4822no—
95#124—4821no—
96#124—2412no—
97#124C2×D24111yescharacteristic
98#120—4822no—
99#120—4821no—
100#104—4822no—
101#104—4821no—
102#101—2411no—
103#101C2×D24112yescomplemented
104C24—4821no—
105#41—9641no—
106#41—4822no—
107#41—4821no—
108C2×Q8—9641no—
109C2×Q8—4821no—
110C2×Q8C22×D24111yescharacteristic
111C2×D4—4821no—
112C2×D4—4822no—
113C2×D4—2412no—
114C2×D4D96411yescharacteristic
115SD16—9642no—
116SD16—9641no—
117D8—9642no—
118D8—9641no—
119M16—22no—
120M16—4821no—
121C22⋊C4—22no—
122C22⋊C4—4822no—
123C22⋊C4—4821no—
124C22⋊C4—4822no—
125C22⋊C4—4822no—
126C42—2412no—
127C42D96411yescharacteristic
128C23—21no—
129C23—19282no—
130C23—19281no—
131C23—4822no—
132Q8—41no—
133Q8—19281no—
134Q8—4822no—
135Q8—4821no—
136D4—41no—
137D4—19281no—
138D4—19282no—
139D4—9642no—
140D4—9641no—
141D4—4822no—
142D4—4821no—
143C2×C4—21no—
144C2×C4—9642no—
145C2×C4—9641no—
146C2×C4—4822no—
147C2×C4D4×D24112yes—
148C2×C4C2×D96411yescharacteristic
149C8—42no—
150C8—9641no—
151C22—42no—
152C22—41no—
153C22—19284no—
154C22—9642no—
155C22—9642no—
156C22—9641no—
157C22—9642no—
158C22#2144061211yescharacteristic
159C4—22no—
160C4—21no—
161C4—41no—
162C4—9642no—
163C4—9641no—
164C2—21no—
165C2—81no—
166C2—19282no—
167C2—19281no—
168C2#2950790511yescharacteristic
subgroupG/H
centerC2#29507905
commutator, cosocleC2×Q8×C241C23
FrattiniC2×Q8C22×D241
Fitting#355×C241C2
socleC2×C241B(4,𝔽2)
hypercenter#355D241
hypocenterC241#2202
LCSG ▷ C2×Q8×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
1. #29508459C2semidirect
2. #29507892C2semidirect
3. #29507889C2semidirect
4. #29507513C2semidirect
5. #355×C241C2semidirect
6. #21440690C22semidirect
16. #21440561C22semidirect
18. #101×C241C22semidirect
84. C241#2202semidirect
90. #355D241semidirect
103. #101C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295084592
#295078922
#295078892
#295075132
#355×C2412
#2202241