Finite Group Databasebeta

← #44506673

Subgroups — #44506673

Order 30848.

212 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 57 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#29508067C211yesmaximal, characteristic, complemented
2#29507997C211yesmaximal, characteristic, complemented
3#29507922C211yesmaximal, characteristic, complemented
4#29507466C211yesmaximal, characteristic, complemented
5D4⋊#14515349C211yesmaximal, characteristic, complemented
6D4⋊#14515349C211yesmaximal, characteristic, complemented
7#555×C241C211yesmaximal, characteristic
8C2×#16838758—21no—
9#21440642C2211yescharacteristic
10#21440575—21no—
11C4⋊#14515349C2211yescharacteristic
12C4⋊#14515349C2211yescharacteristic
13#21440566—22no—
14#21440565—21no—
15#21440563—21no—
16C4×#14515349C2211yescharacteristic
17C4⋊Q8×C241C2211yescharacteristic
18#124×C241—22no—
19#121×C241—21no—
20#121×C241—21no—
21C4×D4×C241C2211yescharacteristic
22C4×D4×C241C2211yescharacteristic
23#117×C241—21no—
24#117×C241—21no—
25C2×Dic482—21no—
26#16838758—42no—
27C2×#14515349—21no—
28C2×#14515349—21no—
29C2×#14515349—21no—
30C4⋊Dic241—21no—
31C4⋊Dic241—21no—
32C2×Q8×C241D412yes—
33C2×D4×C241—22no—
34C2×D4×C241D411yescharacteristic
35C2×D4×C241D411yescharacteristic
36C22×C4×C241—21no—
37C22×C4×C241—21no—
38C4⋊C4×C241—21no—
39C4⋊C4×C241—21no—
40C4⋊C4×C241D411yescharacteristic
41C4⋊C4×C241D411yescharacteristic
42C22⋊C4×C241—22no—
43C22⋊C4×C241—22no—
44C22⋊C4×C241—21no—
45C22⋊C4×C241—21no—
46C42×C241—22no—
47C42×C241C2311yescharacteristic
48Dic482—41no—
49Dic482—41no—
50C2×Dic241—41no—
51#14515349—41no—
52#14515349—41no—
53#14515349—41no—
54C23×C241—21no—
55C23×C241—21no—
56Q8×C241—42no—
57D4×C241—21no—
58D4×C241—21no—
59D4×C241—21no—
60D4×C241—21no—
61D4×C241—82no—
62C2×C4×C241—21no—
63C2×C4×C241—21no—
64C2×C4×C241—22no—
65C2×C4×C241—41no—
66C2×C4×C241—41no—
67C2×C4×C241—41no—
68C2×C4×C241—41no—
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C2×C4×C241C2×D411yescharacteristic
72C22×C241—41no—
73C22×C241—41no—
74C22×C241—41no—
75C22×C241—41no—
76C22×C241—41no—
77C22×C241—41no—
78C22×C241#12011yescharacteristic
79C4×C241—21no—
80C4×C241—41no—
81C4×C241—41no—
82C4×C241—42no—
83C4×C241#13511yescharacteristic
84C4×C241#13511yescharacteristic
85C4×C241AGL(1,ℤ/8)11yescharacteristic
86C4×C241#13711yescharacteristic
87Dic241—81no—
88C2×C241—81no—
89C2×C241—81no—
90C2×C241#44911yescharacteristic
91C2×C241#45211yescharacteristic
92C2×C241#45511yescharacteristic
93C241#164611yescharacteristic, complemented, Sylow
94#1646—2411nomaximal, Sylow
95#555D24111yescharacteristic
96#487—2411no—
97#474—2411no—
98#461—2411no—
99#333—2411no—
100D4⋊C8—2411no—
101D4⋊C8—2411no—
102C2×SD16—4821no—
103C4⋊Q8—2411no—
104C4⋊Q8C2×D24111yescharacteristic
105#124—22no—
106#121—21no—
107#121—21no—
108C4×D4C2×D24111yescharacteristic
109C4×D4C2×D24111yescharacteristic
110#117—21no—
111#117—21no—
112#107—4821no—
113C4⋊C8—2411no—
114C4⋊C8—2411no—
115#103—4822no—
116#103—4821no—
117#102—4821no—
118C4×C8—2411no—
119C2×Q8—4821no—
120C2×Q8C22⋊D24112yes—
121C2×D4—22no—
122C2×D4C22⋊D24111yescharacteristic
123C2×D4C22⋊D24111yescharacteristic
124C22×C4—21no—
125C22×C4—21no—
126SD16—9642no—
127C2×C8—4821no—
128C2×C8—4821no—
129C2×C8—4821no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—4821no—
133C4⋊C4—4821no—
134C4⋊C4C22⋊D24111yescharacteristic
135C4⋊C4C22⋊D24111yescharacteristic
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—22no—
141C42C22×D24111yescharacteristic
142C23—21no—
143C23—21no—
144Q8—42no—
145Q8—9641no—
146Q8—9641no—
147D4—21no—
148D4—21no—
149D4—21no—
150D4—21no—
151D4—82no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—9641no—
160C2×C4C2×C22⋊D24111yescharacteristic
161C2×C4C2×C22⋊D24111yescharacteristic
162C2×C4C2×C22⋊D24111yescharacteristic
163C8—9641no—
164C8—9641no—
165C8—9641no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#2144061111yescharacteristic
173C4—21no—
174C4—41no—
175C4—41no—
176C4—42no—
177C4—19281no—
178C4#2144066211yescharacteristic
179C4#2144066211yescharacteristic
180C4#2144066711yescharacteristic
181C4#2144067211yescharacteristic
182C2—81no—
183C2—81no—
184C2#2950786211yescharacteristic
185C2#2950787911yescharacteristic
186C2#2950789511yescharacteristic
subgroupG/H
centerC22#21440611
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting, prime radical#555×C241C2
socleC22×C241#120
hypercenter#555D241
hypocenterC241#1646
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #29508067C2semidirect
2. #29507997C2semidirect
3. #29507922C2semidirect
4. #29507466C2semidirect
5. D4⋊#14515349C2semidirect
6. D4⋊#14515349C2semidirect
93. C241#1646semidirect

Maximal subgroups

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

subgroupindex
#295080672
#295079972
#295079222
#295074662
D4⋊#145153492
#555×C2412
#1646241