Finite Group Databasebeta

← #44506580

Subgroups — #44506580

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#29508096C211yesmaximal, characteristic, complemented
3#29508013C211yesmaximal, characteristic, complemented
4#29508008C211yesmaximal, characteristic
5#29507447C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic
7#333×C241C211yesmaximal, characteristic, complemented
8C2×#16838760—22no—
9#21440642C2211yescharacteristic
10#21440633—21no—
11#21440622—21no—
12#21440618—22no—
13C4×Dic482C2211yescharacteristic
14C4×D964C2211yescharacteristic
15#21440604—21no—
16C4⋊C4×D241—21no—
17#21440576—21no—
18#21440574—21no—
19#21440567—21no—
20#21440564—21no—
21C4×#14515349C2211yescharacteristic
22C4⋊Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25C2×Dic482—21no—
26C2×Dic482D411yescharacteristic
27C2×D964D411yescharacteristic
28C2×C4×D241—22no—
29C2×C4×D241—21no—
30#16838760—44no—
31C2×#14515349—21no—
32C4⋊Dic241—22no—
33C4⋊Dic241—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241D411yescharacteristic
36C4⋊Dic241D411yescharacteristic
37#16838749—22no—
38#16838749—21no—
39#16838747—22no—
40#16838747—21no—
41C4×Dic241—21no—
42C2×Q8×C241D412yes—
43C2×C8×C241—21no—
44C2×C8×C241—21no—
45C4⋊C4×C241—21no—
46C4⋊C4×C241—21no—
47C42×C241C2311yescharacteristic
48C22×D241—21no—
49Dic482—21no—
50Dic482—21no—
51Dic482—42no—
52D964—21no—
53D964Q1612yescomplemented
54C2×Dic241—21no—
55C2×Dic241—21no—
56C2×Dic241—21no—
57C2×Dic241—41no—
58C4×D241—41no—
59C4×D241—41no—
60C4×D241—82no—
61#14515349—22no—
62Q8×C241—42no—
63C2×C4×C241—22no—
64C2×C4×C241C2×D411yescharacteristic
65C2×C4×C241C2×D411yescharacteristic
66C2×C4×C241C2×D411yescharacteristic
67C8×C241—41no—
68C8×C241—41no—
69C22×C241#12011yescharacteristic
70C2×D241—22no—
71C2×D241—41no—
72C2×D241—41no—
73C4×C241—21no—
74C4×C241—42no—
75C4×C241C2×Q1611yescharacteristic
76C4×C241#13511yescharacteristic
77C4×C241#13711yescharacteristic
78C4×C241#13711yescharacteristic
79Dic241—41no—
80Dic241—41no—
81Dic241—41no—
82Dic241—81no—
83C2×C241#45111yescharacteristic
84C2×C241#45211yescharacteristic
85C2×C241#45311yescharacteristic
86D241—42no—
87C241#163211yescharacteristic, complemented, Sylow
88#1632—2411nomaximal, Sylow
89#554—2411no—
90#494—2411no—
91#477—2411no—
92#476—2411no—
93#333D24111yescharacteristic, complemented
94Q8⋊C8—2411no—
95D4⋊C8—2411no—
96C2×Q16—4822no—
97C4⋊Q8—2411no—
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⋊C8C2×D24111yescharacteristic
109C4⋊C8C2×D24111yescharacteristic
110#103—4821no—
111#102—4821no—
112C4×C8—2411no—
113C2×Q8—4821no—
114C2×Q8—2411no—
115C2×Q8D96412yes—
116C2×D4—2411no—
117C22×C4—4822no—
118C22×C4—4821no—
119Q16—9644no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—4821no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—4822no—
126C4⋊C4—4822no—
127C4⋊C4—4821no—
128C4⋊C4—4821no—
129C4⋊C4—4821no—
130C4⋊C4—2411no—
131C4⋊C4—2411no—
132C22⋊C4—4822no—
133C22⋊C4—4821no—
134C42—4821no—
135C42C22×D24111yescharacteristic
136C23—4821no—
137Q8—42no—
138Q8—9642no—
139Q8—4821no—
140Q8—4821no—
141D4—4821no—
142D4—2412no—
143C2×C4—22no—
144C2×C4—19282no—
145C2×C4—9641no—
146C2×C4—9641no—
147C2×C4—9641no—
148C2×C4—4821no—
149C2×C4—4821no—
150C2×C4—4821no—
151C2×C4D4×D24111yescharacteristic
152C2×C4D4×D24111yescharacteristic
153C2×C4C2×D96411yescharacteristic
154C8—41no—
155C8—41no—
156C8—4822no—
157C22—9641no—
158C22—9641no—
159C22—4822no—
160C22#2144061211yescharacteristic
161C4—21no—
162C4—42no—
163C4—19281no—
164C4—9641no—
165C4—9641no—
166C4—9641no—
167C4Q16×D24111yescharacteristic
168C4#2144066311yescharacteristic
169C4#2144067111yescharacteristic
170C4#2144067411yescharacteristic
171C2—9642no—
172C2#2950787411yescharacteristic
173C2#2950788211yescharacteristic
174C2#2950788711yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#333×C241C2
socleC22×C241#120
prime radicalC2×D964D4
hypercenter#333D241
hypocenterC241#1632
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #29508096C2semidirect
3. #29508013C2semidirect
5. #29507447C2semidirect
7. #333×C241C2semidirect
53. D964Q16semidirect
87. C241#1632semidirect
93. #333D241semidirect

Maximal subgroups

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

subgroupindex
#295084282
#295080962
#295080132
#295080082
#295074472
#295074442
#333×C2412
#1632241