Finite Group Databasebeta

← #44506576

Subgroups — #44506576

Order 30848.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#29508428C211yesmaximal, characteristic
2#29508009C211yesmaximal, characteristic, complemented
3#29508004C211yesmaximal, characteristic
4#29507466C211yesmaximal, characteristic, complemented
5#29507449C211yesmaximal, characteristic, complemented
6#29507446C211yesmaximal, characteristic
7#494×C241C211yesmaximal, characteristic, complemented
8#21440633—21no—
9#21440622—21no—
10#21440618—22no—
11C4×Dic482C2211yescharacteristic
12C4×D964C2211yescharacteristic
13#21440604—21no—
14C4⋊C4×D241—21no—
15#21440575—21no—
16#21440573—21no—
17C4⋊#14515349C2211yescharacteristic
18C4⋊#14515349C2211yescharacteristic
19#21440565—21no—
20#21440562—21no—
21C2×Q16×C241—22no—
22C4⋊Q8×C241C2211yescharacteristic
23C4⋊Q8×C241C2211yescharacteristic
24C4×C8×C241C2211yescharacteristic
25C2×Dic482D411yescharacteristic
26C2×D964D411yescharacteristic
27C2×C4×D241—22no—
28C2×C4×D241—21no—
29C2×#14515349—21no—
30C2×#14515349—21no—
31C4⋊Dic241—22no—
32C4⋊Dic241D411yescharacteristic
33C4⋊Dic241D411yescharacteristic
34#16838749—22no—
35#16838749—21no—
36#16838747—22no—
37#16838747—21no—
38C4×Dic241—21no—
39C2×Q8×C241—21no—
40C2×Q8×C241D412yes—
41Q16×C241—44no—
42C2×C8×C241—21no—
43C4⋊C4×C241—21no—
44C4⋊C4×C241—21no—
45C4⋊C4×C241—21no—
46C4⋊C4×C241—21no—
47C42×C241C2311yescharacteristic
48C22×D241—21no—
49Dic482—21no—
50Dic482—21no—
51D964—21no—
52D964Q1612yescomplemented
53C2×Dic241—21no—
54C2×Dic241—21no—
55C2×Dic241—21no—
56C4×D241—41no—
57C4×D241—41no—
58C4×D241—82no—
59#14515349—41no—
60#14515349—41no—
61Q8×C241—42no—
62Q8×C241—42no—
63C2×C4×C241—22no—
64C2×C4×C241—41no—
65C2×C4×C241C2×D411yescharacteristic
66C2×C4×C241C2×D411yescharacteristic
67C2×C4×C241C2×D411yescharacteristic
68C8×C241—22no—
69C22×C241#12011yescharacteristic
70C2×D241—22no—
71C2×D241—41no—
72C2×D241—41no—
73C4×C241—21no—
74C4×C241—42no—
75C4×C241—81no—
76C4×C241C2×Q1611yescharacteristic
77C4×C241#13511yescharacteristic
78C4×C241#13711yescharacteristic
79C4×C241#13711yescharacteristic
80Dic241—41no—
81Dic241—41no—
82Dic241—41no—
83C2×C241#45111yescharacteristic
84C2×C241#45211yescharacteristic
85C2×C241#45311yescharacteristic
86D241—42no—
87C241#163211yescharacteristic, complemented, Sylow
88#1632—2411nomaximal, Sylow
89#554—2411no—
90#494D24111yescharacteristic, complemented
91#477—2411no—
92#476—2411no—
93#333—2411no—
94Q8⋊C8—2411no—
95D4⋊C8—2411no—
96C2×Q16—22no—
97C4⋊Q8C2×D24111yescharacteristic
98C4⋊Q8C2×D24111yescharacteristic
99#125—4821no—
100C22⋊Q8—4821no—
101C22⋊Q8—4822no—
102C4×Q8—2411no—
103C4×D4—4821no—
104C4×D4—2411no—
105C2×C4⋊C4—4821no—
106#107—4821no—
107#106—4821no—
108C4⋊C8—2411no—
109C4⋊C8—2411no—
110#103—4821no—
111#102—4821no—
112C4×C8C2×D24111yescharacteristic
113C2×Q8—21no—
114C2×Q8—2411no—
115C2×Q8C22⋊D24112yes—
116C2×D4—2411no—
117C22×C4—4822no—
118C22×C4—4821no—
119Q16—44no—
120C2×C8—21no—
121C2×C8—4821no—
122C2×C8—4821no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—4822no—
128C4⋊C4—4822no—
129C4⋊C4—4821no—
130C4⋊C4—2411no—
131C4⋊C4—2411no—
132C22⋊C4—4822no—
133C22⋊C4—4821no—
134C42—4821no—
135C42C22×D24111yescharacteristic
136C23—4821no—
137Q8—42no—
138Q8—42no—
139Q8—4821no—
140Q8—4821no—
141D4—4821no—
142D4—2412no—
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—19282no—
146C2×C4—9641no—
147C2×C4—9641no—
148C2×C4—4821no—
149C2×C4—4821no—
150C2×C4—4821no—
151C2×C4D4×D24111yescharacteristic
152C2×C4D4×D24111yescharacteristic
153C2×C4C2×C22⋊D24111yescharacteristic
154C8—22no—
155C8—9641no—
156C8—9641no—
157C22—9641no—
158C22—9641no—
159C22—4822no—
160C22#2144061011yescharacteristic
161C4—21no—
162C4—42no—
163C4—81no—
164C4—9641no—
165C4—9641no—
166C4—9641no—
167C4Q16×D24111yescharacteristic
168C4#2144066511yescharacteristic
169C4#2144067411yescharacteristic
170C4#2144067411yescharacteristic
171C2—9642no—
172C2#2950787111yescharacteristic
173C2#2950787811yescharacteristic
174C2#2950788411yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#494×C241C2
socleC22×C241#120
prime radicalC2×D964D4
hypercenter#494D241
hypocenterC241#1632
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #29508009C2semidirect
4. #29507466C2semidirect
5. #29507449C2semidirect
7. #494×C241C2semidirect
52. D964Q16semidirect
87. C241#1632semidirect
90. #494D241semidirect

Maximal subgroups

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

subgroupindex
#295084282
#295080092
#295080042
#295074662
#295074492
#295074462
#494×C2412
#1632241