Finite Group Databasebeta

← #44508606

Subgroups — #44508606

Order 30848.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#29508348C211yesmaximal, characteristic
2#29507726C212yesmaximal
3#29507486C211yesmaximal, characteristic
4#29507477C212yesmaximal
5#391×C241C211yesmaximal, characteristic
6C2×#16838754C2212yes—
7#21440641—22no—
8#21440633—22no—
9#21440621—22no—
10#21440601C2212yes—
11#21440566—22no—
12#21440566—22no—
13C22×Q8×C241C2211yescharacteristic
14C2×C4⋊C4×C241C2211yescharacteristic
15C2×C42×C241C2211yescharacteristic
16#95×C241—22no—
17C2×Dic482—22no—
18#16838754—22no—
19#16838754—22no—
20C2×#14515349—22no—
21C4⋊Dic241—22no—
22C4⋊Dic241D412yes—
23C4⋊Dic241D412yes—
24#16838749—24no—
25C22⋊Dic241—22no—
26C4×Dic241—22no—
27C2×Q8×C241—21no—
28C2×Q8×C241—22no—
29C2×Q8×C241—22no—
30C2×Q8×C241Q812yescomplemented
31C22×C4×C241—21no—
32C22×C4×C241—21no—
33C22×C4×C241D412yes—
34C22×C4×C241C2311yescharacteristic
35C4⋊C4×C241—22no—
36C42×C241—22no—
37Dic482—82no—
38C2×Dic241—22no—
39C2×Dic241—22no—
40#14515349—42no—
41C23×C241C2×D411yescharacteristic
42Q8×C241—24no—
43Q8×C241—42no—
44C2×C4×C241—22no—
45C2×C4×C241—22no—
46C2×C4×C241—22no—
47C2×C4×C241—41no—
48C2×C4×C241—41no—
49C2×C4×C241—41no—
50C2×C4×C241—41no—
51C2×C4×C241—42no—
52C2×C4×C241C2×D412yes—
53C2×C4×C241C2×Q811yescharacteristic
54C2×C4×C241#4112yes—
55C2×C4×C241#4111yescharacteristic
56C22×C241—21no—
57C22×C241—21no—
58C22×C241#12011yescharacteristic
59C22×C241C22⋊Q811yescharacteristic
60C22×C241#12411yescharacteristic
61C4×C241—42no—
62C4×C241—42no—
63C4×C241—42no—
64C4×C241C22⋊Q812yes—
65C4×C241#12412yes—
66Dic241—42no—
67Dic241—42no—
68C2×C241—21no—
69C2×C241—21no—
70C2×C241#39311yescharacteristic
71C2×C241#45511yescharacteristic
72C2×C241#45611yescharacteristic
73C241#202811yescharacteristic, complemented, Sylow
74#2028—2411nomaximal, Sylow
75#544—2411no—
76#419—2412no—
77#391D24111yescharacteristic
78#343—2411no—
79#339—2412no—
80C22×Q8C2×D24111yescharacteristic
81C2×M16—2412no—
82C4⋊Q8—4822no—
83#125—4822no—
84C22⋊Q8—4822no—
85#117—2412no—
86C2×C4⋊C4C2×D24111yescharacteristic
87C2×C42C2×D24111yescharacteristic
88#103—4822no—
89#103—4822no—
90#95—22no—
91C2×Q8—21no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8—4822no—
95C2×Q8Dic48212yescomplemented
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D24112yes—
99C22×C4C22×D24111yescharacteristic
100M16—4822no—
101M16—4822no—
102C2×C8—4822no—
103C4⋊C4—22no—
104C4⋊C4—4824no—
105C4⋊C4—4822no—
106C4⋊C4—2412no—
107C4⋊C4—2412no—
108C22⋊C4—4822no—
109C42—22no—
110C42—4822no—
111C23C2×C22⋊D24111yescharacteristic
112Q8—24no—
113Q8—42no—
114Q8—19282no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—4822no—
124C2×C4—4822no—
125C2×C4D4×D24112yes—
126C2×C4C2×Dic48211yescharacteristic
127C2×C4#1683876912yes—
128C2×C4#1683877011yescharacteristic
129C8—9642no—
130C22—21no—
131C22—21no—
132C22#2144061011yescharacteristic
133C22#2144062111yescharacteristic
134C22#2144062911yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—9642no—
139C4—9642no—
140C4#2144061912yes—
141C4#2144062812yes—
142C2—21no—
143C2—21no—
144C2#2950762911yescharacteristic
145C2#2950789411yescharacteristic
146C2#2950789911yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#391×C241C2
socleC22×C241#120
prime radicalC23×C241C2×D4
hypercenter#391D241
hypocenterC241#2028
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C241Q8semidirect
73. C241#2028semidirect
95. C2×Q8Dic482semidirect

Maximal subgroups

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

subgroupindex
#295083482
#295077262
#295074862
#295074772
#391×C2412
#2028241