Finite Group Databasebeta

← #44506132

Subgroups — #44506132

Order 30848.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#29508272C211yesmaximal, characteristic
2#29507739C211yesmaximal, characteristic
3C4⋊C8×D241C211yesmaximal, characteristic
4#29507466C211yesmaximal, characteristic, complemented
5#29507464C211yesmaximal, characteristic, complemented
6#29507462C211yesmaximal, characteristic, complemented
7#333×C241C211yesmaximal, characteristic, complemented
8C2×#16838753—21no—
9C2×C8×D241—21no—
10#21440642C2211yescharacteristic
11#21440633—21no—
12#21440622—21no—
13#21440618C412yes—
14Q8×Dic241C412yes—
15#21440607—21no—
16#21440600—21no—
17C42×D241C2211yescharacteristic
18C4⋊#14515349C2211yescharacteristic
19C4⋊#14515349C2211yescharacteristic
20#21440571—21no—
21#21440571—21no—
22C4⋊Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25C2×Dic482—21no—
26C2×C4×D241C2×C411yescharacteristic
27C2×C4×D241D411yescharacteristic
28C2×C4×D241D411yescharacteristic
29#16838753—42no—
30C2×#14515349—21no—
31C2×#14515349—21no—
32C8×D241—42no—
33C4⋊Dic241—22no—
34C4⋊Dic241—21no—
35C4⋊Dic241C2×C412yes—
36#16838749—22no—
37#16838747—22no—
38C4×Dic241—22no—
39C4×Dic241C2×C411yescharacteristic
40C4×Dic241D411yescharacteristic
41C4×Dic241D411yescharacteristic
42C2×Q8×C241C2×C412yes—
43C2×C8×C241—21no—
44C2×C8×C241—21no—
45C4⋊C4×C241—21no—
46C4⋊C4×C241—21no—
47C42×C241C2311yescharacteristic
48C22×D241C22⋊C411yescharacteristic
49Dic482—41no—
50Dic482—41no—
51C2×Dic241—22no—
52C2×Dic241C22⋊C411yescharacteristic
53C2×Dic241C22⋊C411yescharacteristic
54C2×Dic241C22⋊C411yescharacteristic
55C4×D241—21no—
56C4×D241—21no—
57C4×D241—41no—
58C4×D241SD1612yes—
59C4×D241Q1612yes—
60#14515349—41no—
61#14515349—41no—
62Q8×C241—42no—
63C2×C4×C241—22no—
64C2×C4×C241C22×C411yescharacteristic
65C2×C4×C241C2×D411yescharacteristic
66C2×C4×C241C2×D411yescharacteristic
67C8×C241—41no—
68C8×C241—41no—
69C22×C241C2×C22⋊C411yescharacteristic
70C2×D241—21no—
71C2×D241—21no—
72C2×D241#10312yes—
73C4×C241—21no—
74C4×C241—42no—
75C4×C241C2×SD1611yescharacteristic
76C4×C241C2×Q1611yescharacteristic
77C4×C241AGL(1,ℤ/8)11yescharacteristic
78C4×C241#13711yescharacteristic
79Dic241—21no—
80Dic241—21no—
81Dic241—42no—
82Dic241#10312yes—
83C2×C241#41311yescharacteristic
84C2×C241C2×#10311yescharacteristic
85C2×C241#41711yescharacteristic
86D241—22no—
87C241#155011yescharacteristic, complemented, Sylow
88#1550—2411nomaximal, Sylow
89#533—2411no—
90#423—2411no—
91C2×C4⋊C8—2411no—
92#333—2411no—
93#333D24111yescharacteristic, complemented
94#332—2411no—
95#332—2411no—
96C2×M16—4821no—
97C22×C8—4821no—
98C4⋊Q8—2411no—
99C4⋊Q8C2×D24111yescharacteristic
100#125—4821no—
101C22⋊Q8—4821no—
102C22⋊Q8—2412no—
103C4×Q8—4821no—
104C4×Q8—2412no—
105#117—4821no—
106C2×C42—2411no—
107C4⋊C8—4821no—
108C4⋊C8—4821no—
109C4⋊C8—2411no—
110C4⋊C8—2411no—
111C4⋊C8C2×D24111yescharacteristic
112C4⋊C8C2×D24111yescharacteristic
113C2×Q8—4821no—
114C2×Q8C4×D24112yes—
115C22×C4—2411no—
116C22×C4—2411no—
117C22×C4—2411no—
118M16—9642no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—9642no—
122C2×C8—4821no—
123C2×C8—4821no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—4822no—
127C4⋊C4—4822no—
128C4⋊C4—4821no—
129C4⋊C4—2412no—
130C22⋊C4—4822no—
131C42—4822no—
132C42—2411no—
133C42—2411no—
134C42—2411no—
135C42C22×D24111yescharacteristic
136C23—2411no—
137Q8—42no—
138Q8—9641no—
139Q8—9641no—
140C2×C4—22no—
141C2×C4—9641no—
142C2×C4—4822no—
143C2×C4—4821no—
144C2×C4—4821no—
145C2×C4—2411no—
146C2×C4—2411no—
147C2×C4—2411no—
148C2×C4—2412no—
149C2×C4—2412no—
150C2×C4C2×C4×D24111yescharacteristic
151C2×C4D4×D24111yescharacteristic
152C2×C4D4×D24111yescharacteristic
153C8—41no—
154C8—41no—
155C8—9641no—
156C8—9641no—
157C22—4821no—
158C22—4821no—
159C22—2412no—
160C22C22⋊C4×D24111yescharacteristic
161C4—21no—
162C4—42no—
163C4—9642no—
164C4—4821no—
165C4—4821no—
166C4—2412no—
167C4SD16×D24111yescharacteristic
168C4Q16×D24111yescharacteristic
169C4#2144066911yescharacteristic
170C4#2144067411yescharacteristic
171C2—4822no—
172C2#2950769811yescharacteristic
173C2#103×D24111yescharacteristic
174C2#2950771711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC42C22×D241
Fitting#333×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC22×D241C22⋊C4
cosocleC42×C241C23
hypercenter#333D241
hypocenterC241#1550
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #29507466C2semidirect
5. #29507464C2semidirect
6. #29507462C2semidirect
7. #333×C241C2semidirect
87. C241#1550semidirect
93. #333D241semidirect

Maximal subgroups

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

subgroupindex
#295082722
#295077392
C4⋊C8×D2412
#295074662
#295074642
#295074622
#333×C2412
#1550241