Finite Group Databasebeta

← #44507409

Subgroups — #44507409

Order 30848.

548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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#29507734C212yesmaximal, complemented
2#29507713C212yesmaximal, complemented
3#29507691C211yesmaximal, characteristic, complemented
4#29507684C211yesmaximal, characteristic, complemented
5#585×C241C211yesmaximal, characteristic
6C2×#16838754C2211yescharacteristic, complemented
7C22×#14515349C2211yescharacteristic, complemented
8#21440601C2212yescomplemented
9#21440569—24no—
10#21440566—22no—
11#21440563—22no—
12#21440557—22no—
13C22⋊#14515349—22no—
142−1+4×C241—22no—
152−1+4×C241C412yescomplemented
16H(5,𝔽2)×C241—22no—
17H(5,𝔽2)×C241—22no—
18H(5,𝔽2)×C241C412yescomplemented
19C2×#41×C241—24no—
20C2×#41×C241—22no—
21C2×#41×C241C2212yes—
22C2×#41×C241C2211yescharacteristic
23#16838754—22no—
24C2×#14515349—21no—
25C2×#14515349—21no—
26C2×#14515349—22no—
27C4⋊Dic241—22no—
28C22⋊Dic241—22no—
29C4×Dic241—22no—
30#41×C241—24no—
31#41×C241—28no—
32#41×C241—24no—
33#41×C241—24no—
34#41×C241—24no—
35#41×C241—24no—
36#41×C241—22no—
37#41×C241—22no—
38#41×C241—22no—
39#41×C241—22no—
40#41×C241C2×C414yes—
41#41×C241D414yes—
42C2×Q8×C241—22no—
43C2×Q8×C241—24no—
44C2×Q8×C241C2×C411yescharacteristic
45C2×Q8×C241D412yes—
46C2×D4×C241—28no—
47C2×D4×C241—22no—
48C2×D4×C241—24no—
49C2×D4×C241—22no—
50C2×D4×C241—24no—
51C2×D4×C241C2×C411yescharacteristic
52C2×D4×C241D412yes—
53C2×D4×C241D412yes—
54C22×C4×C241—24no—
55C22×C4×C241—22no—
56C22×C4×C241D412yes—
57C22×C4×C241C2311yescharacteristic
58C2×Dic241—42no—
59#14515349—41no—
60#14515349—41no—
61C23×C241—24no—
62C23×C241—22no—
63C23×C241C22⋊C412yes—
64C23×C241C2×D411yescharacteristic
65Q8×C241—24no—
66Q8×C241—22no—
67Q8×C241—22no—
68Q8×C241C22⋊C414yes—
69D4×C241—28no—
70D4×C241—24no—
71D4×C241—24no—
72D4×C241—24no—
73D4×C241—24no—
74D4×C241—22no—
75D4×C241—22no—
76D4×C241C22⋊C414yes—
77C2×C4×C241—24no—
78C2×C4×C241—28no—
79C2×C4×C241—22no—
80C2×C4×C241—24no—
81C2×C4×C241—24no—
82C2×C4×C241—22no—
83C2×C4×C241—22no—
84C2×C4×C241C22⋊C412yes—
85C2×C4×C241C22×C411yescharacteristic
86C2×C4×C241C2×D412yes—
87C2×C4×C241C2×D412yes—
88C2×C4×C241C2×D411yescharacteristic
89C22×C241—22no—
90C22×C241—24no—
91C22×C241—41no—
92C22×C241—42no—
93C22×C241—82no—
94C22×C241—84no—
95C22×C241C2×C22⋊C411yescharacteristic
96C22×C241#12012yes—
97C4×C241—24no—
98C4×C241—22no—
99C4×C241C2×C22⋊C412yes—
100C4×C241#12011yescharacteristic
101C4×C241#12011yescharacteristic
102Dic241—82no—
103C2×C241—22no—
104C2×C241—21no—
105C2×C241—42no—
106C2×C241—44no—
107C2×C241#37911yescharacteristic
108C241#179411yescharacteristic, complemented, Sylow
109#1794—2411nomaximal, Sylow
110#585D24111yescharacteristic
111#421—2412no—
112#416—2412no—
113#410—2411no—
114#408—2411no—
1152−1+4—22no—
1162−1+4Dic24112yescomplemented
117H(5,𝔽2)—22no—
118H(5,𝔽2)—22no—
119H(5,𝔽2)Dic24112yescomplemented
120C2×#41—24no—
121C2×#41—22no—
122C2×#41C2×D24112yes—
123C2×#41C2×D24111yescharacteristic
124C2×M16—2411no—
125C22×C8—2411no—
126#117—2412no—
127#104—4824no—
128#103—4822no—
129#102—4822no—
130#99—4822no—
131C22⋊C8—4822no—
132#41—24no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—24no—
137#41—24no—
138#41—22no—
139#41—22no—
140#41—22no—
141#41—22no—
142#41C2×Dic24114yes—
143#41C22⋊D24114yes—
144C2×Q8—22no—
145C2×Q8—24no—
146C2×Q8C2×Dic24111yescharacteristic
147C2×Q8C22⋊D24112yes—
148C2×D4—28no—
149C2×D4—22no—
150C2×D4—24no—
151C2×D4—22no—
152C2×D4—24no—
153C2×D4C2×Dic24111yescharacteristic
154C2×D4C22⋊D24112yes—
155C2×D4C22⋊D24112yes—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4C22⋊D24112yes—
159C22×C4C22×D24111yescharacteristic
160M16—4822no—
161C2×C8—4821no—
162C2×C8—4821no—
163C2×C8—4822no—
164C4⋊C4—4822no—
165C22⋊C4—4822no—
166C42—4822no—
167C23—24no—
168C23—22no—
169C23C22⋊Dic24112yes—
170C23C2×C22⋊D24111yescharacteristic
171Q8—24no—
172Q8—22no—
173Q8—22no—
174Q8C22⋊Dic24114yes—
175D4—28no—
176D4—24no—
177D4—24no—
178D4—24no—
179D4—24no—
180D4—22no—
181D4—22no—
182D4C22⋊Dic24114yes—
183C2×C4—24no—
184C2×C4—28no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—9642no—
191C2×C4C22⋊Dic24112yes—
192C2×C4C22×Dic24111yescharacteristic
193C2×C4C2×C22⋊D24112yes—
194C2×C4C2×C22⋊D24112yes—
195C2×C4C2×C22⋊D24111yescharacteristic
196C8—9641no—
197C8—9641no—
198C22—22no—
199C22—24no—
200C22—41no—
201C22—42no—
202C22—82no—
203C22—84no—
204C22C2×C22⋊Dic24111yescharacteristic
205C22#2144061112yes—
206C4—24no—
207C4—22no—
208C4—19282no—
209C4C2×C22⋊Dic24112yes—
210C4#2144061111yescharacteristic
211C4#2144061111yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—44no—
216C2#2950757311yescharacteristic
subgroupG/H
centerC4#21440611
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting, prime radical#585×C241C2
socleC2×C241#379
cosocleC22×C4×C241C23
hypercenter#585D241
hypocenterC241#1794
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #29507734C2semidirect
2. #29507713C2semidirect
3. #29507691C2semidirect
4. #29507684C2semidirect
6. C2×#16838754C22semidirect
7. C22×#14515349C22semidirect
8. #21440601C22semidirect
15. 2−1+4×C241C4semidirect
18. H(5,𝔽2)×C241C4semidirect
108. C241#1794semidirect
116. 2−1+4Dic241semidirect
119. H(5,𝔽2)Dic241semidirect

Maximal subgroups

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

subgroupindex
#295077342
#295077132
#295076912
#295076842
#585×C2412
#1794241