Finite Group Databasebeta

← #37572484

Subgroups — #37572484

Order 24448.

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#27132680C212yesmaximal, complemented
2#27132659C212yesmaximal, complemented
3#27132637C211yesmaximal, characteristic, complemented
4#27132630C211yesmaximal, characteristic, complemented
5#585×C191C211yesmaximal, characteristic
6C2×#15690271C2211yescharacteristic, complemented
7C22×C191⋊C8C2211yescharacteristic, complemented
8#20259281C2212yescomplemented
9#20259249—24no—
10#20259246—22no—
11#20259243—22no—
12#20259237—22no—
13C22⋊(C191⋊C8)—22no—
142−1+4×C191—22no—
152−1+4×C191C412yescomplemented
16H(5,𝔽2)×C191—22no—
17H(5,𝔽2)×C191—22no—
18H(5,𝔽2)×C191C412yescomplemented
19C2×#41×C191—24no—
20C2×#41×C191—22no—
21C2×#41×C191C2212yes—
22C2×#41×C191C2211yescharacteristic
23#15690271—22no—
24C2×C191⋊C8—21no—
25C2×C191⋊C8—21no—
26C2×C191⋊C8—22no—
27C4⋊Dic191—22no—
28C22⋊Dic191—22no—
29C4×Dic191—22no—
30#41×C191—24no—
31#41×C191—28no—
32#41×C191—24no—
33#41×C191—24no—
34#41×C191—24no—
35#41×C191—24no—
36#41×C191—22no—
37#41×C191—22no—
38#41×C191—22no—
39#41×C191—22no—
40#41×C191C2×C414yes—
41#41×C191D414yes—
42C2×Q8×C191—22no—
43C2×Q8×C191—24no—
44C2×Q8×C191C2×C411yescharacteristic
45C2×Q8×C191D412yes—
46C2×D4×C191—28no—
47C2×D4×C191—22no—
48C2×D4×C191—24no—
49C2×D4×C191—22no—
50C2×D4×C191—24no—
51C2×D4×C191C2×C411yescharacteristic
52C2×D4×C191D412yes—
53C2×D4×C191D412yes—
54C22×C4×C191—24no—
55C22×C4×C191—22no—
56C22×C4×C191D412yes—
57C22×C4×C191C2311yescharacteristic
58C2×Dic191—42no—
59C191⋊C8—41no—
60C191⋊C8—41no—
61C23×C191—24no—
62C23×C191—22no—
63C23×C191C22⋊C412yes—
64C23×C191C2×D411yescharacteristic
65Q8×C191—24no—
66Q8×C191—22no—
67Q8×C191—22no—
68Q8×C191C22⋊C414yes—
69D4×C191—28no—
70D4×C191—24no—
71D4×C191—24no—
72D4×C191—24no—
73D4×C191—24no—
74D4×C191—22no—
75D4×C191—22no—
76D4×C191C22⋊C414yes—
77C2×C4×C191—24no—
78C2×C4×C191—28no—
79C2×C4×C191—22no—
80C2×C4×C191—24no—
81C2×C4×C191—24no—
82C2×C4×C191—22no—
83C2×C4×C191—22no—
84C2×C4×C191C22⋊C412yes—
85C2×C4×C191C22×C411yescharacteristic
86C2×C4×C191C2×D412yes—
87C2×C4×C191C2×D412yes—
88C2×C4×C191C2×D411yescharacteristic
89C22×C191—22no—
90C22×C191—24no—
91C22×C191—41no—
92C22×C191—42no—
93C22×C191—82no—
94C22×C191—84no—
95C22×C191C2×C22⋊C411yescharacteristic
96C22×C191#12012yes—
97C4×C191—24no—
98C4×C191—22no—
99C4×C191C2×C22⋊C412yes—
100C4×C191#12011yescharacteristic
101C4×C191#12011yescharacteristic
102Dic191—82no—
103C2×C191—22no—
104C2×C191—21no—
105C2×C191—42no—
106C2×C191—44no—
107C2×C191#37911yescharacteristic
108C191#179411yescharacteristic, complemented, Sylow
109#1794—1911nomaximal, Sylow
110#585D19111yescharacteristic
111#421—1912no—
112#416—1912no—
113#410—1911no—
114#408—1911no—
1152−1+4—22no—
1162−1+4Dic19112yescomplemented
117H(5,𝔽2)—22no—
118H(5,𝔽2)—22no—
119H(5,𝔽2)Dic19112yescomplemented
120C2×#41—24no—
121C2×#41—22no—
122C2×#41C2×D19112yes—
123C2×#41C2×D19111yescharacteristic
124C2×M16—1911no—
125C22×C8—1911no—
126#117—1912no—
127#104—3824no—
128#103—3822no—
129#102—3822no—
130#99—3822no—
131C22⋊C8—3822no—
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×Dic19114yes—
143#41C22⋊D19114yes—
144C2×Q8—22no—
145C2×Q8—24no—
146C2×Q8C2×Dic19111yescharacteristic
147C2×Q8C22⋊D19112yes—
148C2×D4—28no—
149C2×D4—22no—
150C2×D4—24no—
151C2×D4—22no—
152C2×D4—24no—
153C2×D4C2×Dic19111yescharacteristic
154C2×D4C22⋊D19112yes—
155C2×D4C22⋊D19112yes—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4C22⋊D19112yes—
159C22×C4C22×D19111yescharacteristic
160M16—3822no—
161C2×C8—3821no—
162C2×C8—3821no—
163C2×C8—3822no—
164C4⋊C4—3822no—
165C22⋊C4—3822no—
166C42—3822no—
167C23—24no—
168C23—22no—
169C23C22⋊Dic19112yes—
170C23C2×C22⋊D19111yescharacteristic
171Q8—24no—
172Q8—22no—
173Q8—22no—
174Q8C22⋊Dic19114yes—
175D4—28no—
176D4—24no—
177D4—24no—
178D4—24no—
179D4—24no—
180D4—22no—
181D4—22no—
182D4C22⋊Dic19114yes—
183C2×C4—24no—
184C2×C4—28no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—7642no—
191C2×C4C22⋊Dic19112yes—
192C2×C4C22×Dic19111yescharacteristic
193C2×C4C2×C22⋊D19112yes—
194C2×C4C2×C22⋊D19112yes—
195C2×C4C2×C22⋊D19111yescharacteristic
196C8—7641no—
197C8—7641no—
198C22—22no—
199C22—24no—
200C22—41no—
201C22—42no—
202C22—82no—
203C22—84no—
204C22C2×C22⋊Dic19111yescharacteristic
205C22#2025929112yes—
206C4—24no—
207C4—22no—
208C4—15282no—
209C4C2×C22⋊Dic19112yes—
210C4#2025929111yescharacteristic
211C4#2025929111yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—44no—
216C2#2713251911yescharacteristic
subgroupG/H
centerC4#20259291
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting, prime radical#585×C191C2
socleC2×C191#379
cosocleC22×C4×C191C23
hypercenter#585D191
hypocenterC191#1794
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #27132680C2semidirect
2. #27132659C2semidirect
3. #27132637C2semidirect
4. #27132630C2semidirect
6. C2×#15690271C22semidirect
7. C22×C191⋊C8C22semidirect
8. #20259281C22semidirect
15. 2−1+4×C191C4semidirect
18. H(5,𝔽2)×C191C4semidirect
108. C191#1794semidirect
116. 2−1+4Dic191semidirect
119. H(5,𝔽2)Dic191semidirect

Maximal subgroups

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

subgroupindex
#271326802
#271326592
#271326372
#271326302
#585×C1912
#1794191