Finite Group Databasebeta

← #44505955

Subgroups — #44505955

Order 30848.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#29508269C211yesmaximal, characteristic
2#29507771C211yesmaximal, characteristic
3#29507562C211yesmaximal, characteristic
4#29507455C211yesmaximal, characteristic
5#29507454C211yesmaximal, characteristic
6#29507453C211yesmaximal, characteristic
7#328×C241C211yesmaximal, characteristic
8#21440641C411yescharacteristic, complemented
9#21440640C411yescharacteristic, complemented
10#21440632—21no—
11#21440621C2211yescharacteristic
12#21440619—21no—
13Q8×Dic241C411yescharacteristic, complemented
14#21440607—21no—
15#21440607C411yescharacteristic, complemented
16#21440598—21no—
17C2×C4×Dic241—21no—
18C2×C4×Dic241C2211yescharacteristic
19#21440571—21no—
20C22⋊#14515349C2211yescharacteristic
21#21440552—21no—
22#21440549—21no—
23#21440549C2211yescharacteristic
24C22⋊Q8×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27C2×Dic482—21no—
28C2×Dic482C2×C411yescharacteristic
29C22×Dic241—21no—
30C22×Dic241D411yescharacteristic
31C22×Dic241D411yescharacteristic
32C2×#14515349—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241C2×C411yescharacteristic
35#16838749—21no—
36#16838749—21no—
37#16838749—21no—
38#16838749—21no—
39#16838749—21no—
40C22⋊Dic241—21no—
41C4×Dic241—24no—
42C4×Dic241—21no—
43C4×Dic241—21no—
44C4×Dic241C2×C411yescharacteristic
45C4×Dic241C2×C411yescharacteristic
46C4×Dic241D411yescharacteristic
47C4×Dic241D411yescharacteristic
48C2×Q8×C241C2×C411yescharacteristic
49C22×C4×C241—21no—
50C22×C4×C241C2311yescharacteristic
51C2×C8×C241—21no—
52C4⋊C4×C241—21no—
53C4⋊C4×C241C2×C411yescharacteristic
54C22⋊C4×C241—21no—
55Dic482—42no—
56Dic482—41no—
57C2×Dic241—21no—
58C2×Dic241—21no—
59C2×Dic241—22no—
60C2×Dic241—22no—
61C2×Dic241—21no—
62C2×Dic241—21no—
63C2×Dic241—41no—
64C2×Dic241—41no—
65C2×Dic241C22⋊C411yescharacteristic
66C2×Dic241C22⋊C411yescharacteristic
67C2×Dic241C22⋊C411yescharacteristic
68C2×Dic241C22⋊C411yescharacteristic
69#14515349—41no—
70C23×C241C2×D411yescharacteristic
71Q8×C241—41no—
72C2×C4×C241—22no—
73C2×C4×C241—21no—
74C2×C4×C241—21no—
75C2×C4×C241—41no—
76C2×C4×C241—41no—
77C2×C4×C241—41no—
78C2×C4×C241C22×C411yescharacteristic
79C2×C4×C241C2×D411yescharacteristic
80C8×C241—41no—
81C22×C241—21no—
82C22×C241—21no—
83C22×C241C2×C22⋊C411yescharacteristic
84C22×C241#13711yescharacteristic
85C22×C241#13711yescharacteristic
86C4×C241—21no—
87C4×C241—21no—
88C4×C241—42no—
89C4×C241—41no—
90C4×C241—41no—
91Dic241—21no—
92Dic241—21no—
93Dic241—21no—
94Dic241—42no—
95Dic241—41no—
96Dic241—41no—
97Dic241#10412yes—
98C2×C241—21no—
99C2×C241—21no—
100C2×C241#41011yescharacteristic
101C2×C241#41911yescharacteristic
102C2×C241C2×#10411yescharacteristic
103C241#150611yescharacteristic, complemented, Sylow
104#1506—2411nomaximal, Sylow
105#533—2411no—
106#432—2411no—
107#376—2411no—
108#328—2411no—
109#328—2411no—
110#328—2411no—
111#328D24111yescharacteristic
112C4⋊Q8—2411no—
113C4⋊Q8—2411no—
114#125—4821no—
115C22⋊Q8—4821no—
116C22⋊Q8—2411no—
117C22⋊Q8C2×D24111yescharacteristic
118C4×Q8—4821no—
119C4×Q8—2411no—
120C4×Q8—2411no—
121#117—4821no—
122C2×C42—4821no—
123C2×C42—2411no—
124C4⋊C8—4821no—
125C22⋊C8—2411no—
126C22⋊C8C2×D24111yescharacteristic
127#97—4821no—
128#95—4821no—
129#95—2411no—
130#95C2×D24111yescharacteristic
131C2×Q8—4821no—
132C2×Q8—2411no—
133C2×Q8C4×D24111yescharacteristic
134C22×C4—21no—
135C22×C4—4821no—
136C22×C4—2411no—
137C22×C4—2411no—
138C22×C4C22×D24111yescharacteristic
139C2×C8—21no—
140C2×C8—4821no—
141C4⋊C4—21no—
142C4⋊C4—4821no—
143C4⋊C4—4821no—
144C4⋊C4—4821no—
145C4⋊C4—4821no—
146C4⋊C4—4821no—
147C4⋊C4—4821no—
148C4⋊C4—2411no—
149C4⋊C4C4×D24111yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—4821no—
152C42—4824no—
153C42—4821no—
154C42—4821no—
155C42—2411no—
156C42—2411no—
157C42—2411no—
158C42—2411no—
159C23D4×D24111yescharacteristic
160Q8—41no—
161Q8—9641no—
162Q8—9642no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—9641no—
170C2×C4—9641no—
171C2×C4—4822no—
172C2×C4—4821no—
173C2×C4—4821no—
174C2×C4—4821no—
175C2×C4—4821no—
176C2×C4—4822no—
177C2×C4—2411no—
178C2×C4—2411no—
179C2×C4—2411no—
180C2×C4—2411no—
181C2×C4C2×C4×D24111yescharacteristic
182C2×C4D4×D24111yescharacteristic
183C8—41no—
184C8—9641no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D24111yescharacteristic
188C22#2144067111yescharacteristic
189C22#2144067411yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—41no—
194C4—41no—
195C4—9642no—
196C4—9641no—
197C4—9641no—
198C4—4821no—
199C4—4821no—
200C4—4821no—
201C4—2412no—
202C2—21no—
203C2—21no—
204C2#2950768911yescharacteristic
205C2#2950772411yescharacteristic
206C2#104×D24111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#328×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC23×C241C2×D4
cosocleC22×C4×C241C23
hypercenter#328D241
hypocenterC241#1506
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #21440641C4semidirect
9. #21440640C4semidirect
13. Q8×Dic241C4semidirect
15. #21440607C4semidirect
103. C241#1506semidirect

Maximal subgroups

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

subgroupindex
#295082692
#295077712
#295075622
#295074552
#295074542
#295074532
#328×C2412
#1506241