Finite Group Databasebeta

← #44505942

Subgroups — #44505942

Order 30848.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#29507767C211yesmaximal, characteristic
3#29507568C211yesmaximal, 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×#16838749—21no—
18C2×C4×Dic241—21no—
19C2×C4×Dic241C2211yescharacteristic
20#21440571—21no—
21C22⋊#14515349C2211yescharacteristic
22C8×Dic241—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—24no—
36#16838749—21no—
37#16838749—21no—
38#16838749—21no—
39#16838749—21no—
40#16838749—21no—
41C22⋊Dic241—21no—
42C4×Dic241—21no—
43C4×Dic241—21no—
44C4×Dic241—42no—
45C4×Dic241C2×C411yescharacteristic
46C4×Dic241C2×C411yescharacteristic
47C4×Dic241D411yescharacteristic
48C4×Dic241D411yescharacteristic
49C2×Q8×C241C2×C411yescharacteristic
50C22×C4×C241—21no—
51C22×C4×C241C2311yescharacteristic
52C2×C8×C241—21no—
53C4⋊C4×C241—21no—
54C4⋊C4×C241C2×C411yescharacteristic
55C22⋊C4×C241—21no—
56Dic482—42no—
57Dic482—41no—
58C2×Dic241—22no—
59C2×Dic241—22no—
60C2×Dic241—21no—
61C2×Dic241—21no—
62C2×Dic241—41no—
63C2×Dic241—41no—
64C2×Dic241C22⋊C411yescharacteristic
65C2×Dic241C22⋊C411yescharacteristic
66C2×Dic241C22⋊C411yescharacteristic
67C2×Dic241C22⋊C411yescharacteristic
68C2×Dic241SD1612yes—
69C2×Dic241Q1612yes—
70#14515349—41no—
71C23×C241C2×D411yescharacteristic
72Q8×C241—41no—
73C2×C4×C241—22no—
74C2×C4×C241—21no—
75C2×C4×C241—21no—
76C2×C4×C241—41no—
77C2×C4×C241—41no—
78C2×C4×C241—41no—
79C2×C4×C241C22×C411yescharacteristic
80C2×C4×C241C2×D411yescharacteristic
81C8×C241—41no—
82C22×C241—21no—
83C22×C241—21no—
84C22×C241C2×C22⋊C411yescharacteristic
85C22×C241C2×SD1611yescharacteristic
86C22×C241C2×Q1611yescharacteristic
87C4×C241—21no—
88C4×C241—21no—
89C4×C241—42no—
90C4×C241—41no—
91C4×C241—41no—
92Dic241—21no—
93Dic241—42no—
94Dic241—41no—
95Dic241—41no—
96Dic241#10312yes—
97Dic241#10312yes—
98Dic241#10412yes—
99C2×C241—21no—
100C2×C241—21no—
101C2×C241#41011yescharacteristic
102C2×C241C2×#10311yescharacteristic
103C2×C241C2×#10411yescharacteristic
104C241#150311yescharacteristic, complemented, Sylow
105#1503—2411nomaximal, Sylow
106#533—2411no—
107#431—2411no—
108C4×C4⋊C4—2411no—
109#328—2411no—
110#328—2411no—
111#328—2411no—
112#328D24111yescharacteristic
113C4⋊Q8—2411no—
114C4⋊Q8—2411no—
115#125—4821no—
116C22⋊Q8—4821no—
117C22⋊Q8—2411no—
118C22⋊Q8C2×D24111yescharacteristic
119C4×Q8—4821no—
120C4×Q8—2411no—
121C4×Q8—2411no—
122#117—4821no—
123C2×C4⋊C4—4821no—
124C2×C42—4821no—
125C2×C42—2411no—
126C4⋊C8—4821no—
127C22⋊C8—2411no—
128C22⋊C8C2×D24111yescharacteristic
129C4×C8—4821no—
130#95—2411no—
131#95C2×D24111yescharacteristic
132C2×Q8—4821no—
133C2×Q8—2411no—
134C2×Q8C4×D24111yescharacteristic
135C22×C4—21no—
136C22×C4—4821no—
137C22×C4—2411no—
138C22×C4—2411no—
139C22×C4C22×D24111yescharacteristic
140C2×C8—21no—
141C2×C8—4821no—
142C4⋊C4—21no—
143C4⋊C4—4824no—
144C4⋊C4—4821no—
145C4⋊C4—4821no—
146C4⋊C4—4821no—
147C4⋊C4—4821no—
148C4⋊C4—4821no—
149C4⋊C4—4821no—
150C4⋊C4—2411no—
151C4⋊C4C4×D24111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—4821no—
154C42—9642no—
155C42—4821no—
156C42—4821no—
157C42—2411no—
158C42—2411no—
159C42—2411no—
160C42—2411no—
161C23D4×D24111yescharacteristic
162Q8—41no—
163Q8—9641no—
164Q8—9642no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—9641no—
172C2×C4—9641no—
173C2×C4—4822no—
174C2×C4—4821no—
175C2×C4—4821no—
176C2×C4—4822no—
177C2×C4—2411no—
178C2×C4—2411no—
179C2×C4—2411no—
180C2×C4—2411no—
181C2×C4—2412no—
182C2×C4—2412no—
183C2×C4C2×C4×D24111yescharacteristic
184C2×C4D4×D24111yescharacteristic
185C8—41no—
186C8—9641no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D24111yescharacteristic
190C22SD16×D24111yescharacteristic
191C22Q16×D24111yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—9642no—
198C4—9641no—
199C4—9641no—
200C4—4821no—
201C4—2412no—
202C4—2412no—
203C4—2412no—
204C2—21no—
205C2—21no—
206C2#2950768911yescharacteristic
207C2#103×D24111yescharacteristic
208C2#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#1503
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
104. C241#1503semidirect

Maximal subgroups

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

subgroupindex
#295082692
#295077672
#295075682
#295074552
#295074542
#295074532
#328×C2412
#1503241