Finite Group Databasebeta

← #44508586

Subgroups — #44508586

Order 30848.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#21440642C211yesmaximal, characteristic
2C2×#21440566C212yesmaximal
3#29507479C212yesmaximal
4#29507472C211yesmaximal, characteristic
5#391×C241C211yesmaximal, characteristic
6C22×Dic482—21no—
7C22×#14515349C2212yes—
8#21440642—24no—
9C2×C4⋊Dic241—21no—
10C2×C4⋊Dic241C2212yes—
11#21440566—24no—
12C22×Q8×C241C2211yescharacteristic
13C2×C4⋊C4×C241C2211yescharacteristic
14C2×C42×C241C2211yescharacteristic
15#95×C241—21no—
16#95×C241—21no—
17C2×Dic482—24no—
18C2×Dic482—42no—
19C2×Dic482—42no—
20C22×Dic241—22no—
21C2×#14515349—22no—
22C2×#14515349—22no—
23C2×#14515349—22no—
24C4⋊Dic241—24no—
25C4⋊Dic241—22no—
26C4⋊Dic241D414yes—
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×C241D411yescharacteristic
34C22×C4×C241D411yescharacteristic
35C22×C4×C241C2311yescharacteristic
36C4⋊C4×C241—22no—
37C42×C241—22no—
38Dic482—48no—
39C2×Dic241—24no—
40C2×Dic241—42no—
41C2×Dic241—42no—
42#14515349—42no—
43C23×C241C2×D411yescharacteristic
44Q8×C241—24no—
45Q8×C241—42no—
46C2×C4×C241—21no—
47C2×C4×C241—21no—
48C2×C4×C241—21no—
49C2×C4×C241—21no—
50C2×C4×C241—22no—
51C2×C4×C241—41no—
52C2×C4×C241—41no—
53C2×C4×C241—41no—
54C2×C4×C241—41no—
55C2×C4×C241—41no—
56C2×C4×C241SD1612yes—
57C2×C4×C241Q1612yes—
58C2×C4×C241C2×D412yes—
59C2×C4×C241C2×Q811yescharacteristic
60C2×C4×C241#4112yes—
61C2×C4×C241#4111yescharacteristic
62C22×C241#12011yescharacteristic
63C22×C241C22⋊Q811yescharacteristic
64C22×C241#12411yescharacteristic
65C22×C241C2×SD1611yescharacteristic
66C22×C241C2×Q1611yescharacteristic
67C22×C241AGL(1,ℤ/8)11yescharacteristic
68C22×C241#13711yescharacteristic
69C4×C241—22no—
70C4×C241—22no—
71C4×C241—42no—
72C4×C241—81no—
73C4×C241C22⋊Q812yes—
74C4×C241#12412yes—
75Dic241—44no—
76C2×C241#39311yescharacteristic
77C2×C241#45011yescharacteristic
78C2×C241#45111yescharacteristic
79C2×C241#47511yescharacteristic
80C2×C241#47711yescharacteristic
81C2×C241#48711yescharacteristic
82C2×C241#48911yescharacteristic
83C241#202411yescharacteristic, complemented, Sylow
84#2024—2411nomaximal, Sylow
85C2×C4⋊Q8—2411no—
86C2×#103—2412no—
87#391D24111yescharacteristic
88#340—2412no—
89#336—2411no—
90C22×Q8—4821no—
91C22×Q8C2×D24111yescharacteristic
92C22×C8—2412no—
93C4⋊Q8—4824no—
94C2×C4⋊C4—4821no—
95C2×C4⋊C4—2412no—
96C2×C4⋊C4C2×D24111yescharacteristic
97C2×C42C2×D24111yescharacteristic
98#103—4824no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—9642no—
105C2×Q8—9642no—
106C2×Q8—4824no—
107C2×Q8Dic48212yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—4822no—
111C22×C4C22⋊D24111yescharacteristic
112C22×C4C22⋊D24111yescharacteristic
113C22×C4C22×D24111yescharacteristic
114C2×C8—4822no—
115C2×C8—4822no—
116C2×C8—4822no—
117C4⋊C4—22no—
118C4⋊C4—4824no—
119C4⋊C4—4822no—
120C4⋊C4—2414no—
121C42—22no—
122C23C2×C22⋊D24111yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—9648no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—9642no—
137C2×C4—9642no—
138C2×C4—4824no—
139C2×C4#1683875712yes—
140C2×C4#1683876012yes—
141C2×C4D4×D24112yes—
142C2×C4C2×Dic48211yescharacteristic
143C2×C4#1683876912yes—
144C2×C4#1683877011yescharacteristic
145C8—9642no—
146C22#2144061011yescharacteristic
147C22#2144062111yescharacteristic
148C22#2144062911yescharacteristic
149C22C2×#1683875711yescharacteristic
150C22C2×#1683876011yescharacteristic
151C22#2144066711yescharacteristic
152C22#2144067211yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—9644no—
158C4#2144061912yes—
159C4#2144062812yes—
160C2#2950762911yescharacteristic
161C2#2950786711yescharacteristic
162C2#2950787211yescharacteristic
163C2#2950800211yescharacteristic
164C2#2950801211yescharacteristic
165C2#2950806711yescharacteristic
166C2#2950807611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D241
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#391×C241C2
socle, prime radicalC23×C241C2×D4
hypercenter#391D241
hypocenterC241#2024
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C241Q8semidirect
83. C241#2024semidirect
107. C2×Q8Dic482semidirect

Maximal subgroups

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

subgroupindex
C2×#214406422
C2×#214405662
#295074792
#295074722
#391×C2412
#2024241