Finite Group Databasebeta

← #37582984

Subgroups — #37582984

Order 24448.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#20259353C212yesmaximal, complemented
2C2×#20259348C212yesmaximal, complemented
3#27133213C211yesmaximal, characteristic, complemented
4#27133058C212yesmaximal, complemented
5#27133053C212yesmaximal, complemented
6#27133045C214yesmaximal, complemented
7C4×#15690271C211yesmaximal, characteristic, complemented
8C2×#124×C191C211yesmaximal, characteristic, complemented
9C2×#15690287C2212yes—
10#20259353—28no—
11#20259348—28no—
12C2×#15690277C2214yescomplemented
13C2×#15690275C2214yes—
14C2×#15690274C2214yescomplemented
15C2×#15690272C2214yes—
16C2×#15690271C2212yes—
17#20259322C2211yescharacteristic, complemented
18#20259319C2211yescharacteristic, complemented
19#20259310C2212yescomplemented
20#20259296—22no—
21C4×D764—22no—
22#20259233C2212yescomplemented
23C4×C191⋊C8C2212yescomplemented
24C22×Q8×C191C2211yescharacteristic
25C22×D4×C191C2211yescharacteristic
26#124×C191—22no—
27#124×C191C2212yes—
28#124×C191C2212yes—
29C2×C22⋊C4×C191—22no—
30C2×C42×C191C2211yescharacteristic
31#15690287—24no—
32#15690287—24no—
33C2×Dic382C2312yes—
34C2×D764—22no—
35C2×D764C2312yes—
36C2×C22⋊D191—22no—
37C2×C4×D191—22no—
38#15690277—28no—
39#15690275—28no—
40#15690274—28no—
41#15690272—28no—
42#15690271D418yescomplemented
43C2×C191⋊C8C2314yes—
44C4⋊Dic191—22no—
45(C2×D191)⋊C4—24no—
46C24×C191—21no—
47C2×Q8×C191—21no—
48C2×Q8×C191—24no—
49C2×Q8×C191C2312yes—
50C2×D4×C191—24no—
51C2×D4×C191—21no—
52C2×D4×C191C2312yes—
53C22×C4×C191—21no—
54C22×C4×C191D412yes—
55C22×C4×C191C2311yescharacteristic
56C22⋊C4×C191—24no—
57C22⋊C4×C191—24no—
58C42×C191D412yes—
59C42×C191C2311yescharacteristic
60C42×C191C2311yescharacteristic
61C22×D191—22no—
62Dic382—22no—
63Dic382—22no—
64D764—22no—
65D764—22no—
66D764—44no—
67C22⋊D191—44no—
68C2×Dic191—22no—
69C4×D191—44no—
70C191⋊C8C2×D418yes—
71C23×C191—22no—
72C23×C191—44no—
73C23×C191—42no—
74C23×C191C2×D411yescharacteristic
75Q8×C191—24no—
76Q8×C191—42no—
77D4×C191—24no—
78D4×C191—42no—
79C2×C4×C191—22no—
80C2×C4×C191—42no—
81C2×C4×C191—42no—
82C2×C4×C191C2×D414yes—
83C2×C4×C191C2×D412yes—
84C2×C4×C191C2×D412yes—
85C2×C4×C191C2×D411yescharacteristic
86C2×C4×C191C2411yescharacteristic
87C22×C191—22no—
88C22×C191—42no—
89C22×C191—44no—
90C22×C191—84no—
91C22×C191#12712yes—
92C22×C191C22×D411yescharacteristic
93C2×D191—42no—
94C2×D191—44no—
95C4×C191—22no—
96C4×C191—22no—
97C4×C191—42no—
98C4×C191#12712yes—
99C4×C191C22×D412yes—
100Dic191—42no—
101C2×C191—22no—
102C2×C191—82no—
103C2×C191C2×#12711yescharacteristic
104C2×C191#57512yes—
105D191—82no—
106C191#315311yescharacteristic, complemented, Sylow
107#3153—1911nomaximal, Sylow
108C2×#137—1912no—
109C2×AGL(1,ℤ/8)—1912no—
110#532—1911no—
111C2×#124D19111yescharacteristic, complemented
112#497—1912no—
113#496—1912no—
114#495—1914no—
115C4×M16—1911no—
116C2×#41—1912no—
117C22×Q8C2×D19111yescharacteristic
118C22×D4C2×D19111yescharacteristic
119#137—3828no—
120AGL(1,ℤ/8)—3828no—
121C2×Q16—1914no—
122C2×SD16—1914no—
123C2×SD16—1914no—
124C2×D8—1914no—
125C2×M16—1912no—
126C4⋊Q8—1911no—
127#127—1911no—
128#124—22no—
129#124—1912no—
130#124C2×D19112yes—
131#124C2×D19112yes—
132#121—3822no—
133C4×D4—3822no—
134C2×C22⋊C4—22no—
135C2×C42C2×D19111yescharacteristic
136#97—1912no—
137C4×C8—1912no—
138C24—21no—
139#41—3824no—
140#41—3824no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—1912no—
144C2×Q8C22×D19112yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—3822no—
148C2×D4—3822no—
149C2×D4—1912no—
150C2×D4C22×D19112yes—
151C22×C4—21no—
152C22×C4—3822no—
153C22×C4C22⋊D19112yes—
154C22×C4C22×D19111yescharacteristic
155Q16—3828no—
156SD16—3828no—
157SD16—3828no—
158D8—3828no—
159M16—1918no—
160C2×C8—1914no—
161C4⋊C4—3822no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—3824no—
165C42C22⋊D19112yes—
166C42C22×D19111yescharacteristic
167C42C22×D19111yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—3822no—
172C23C2×C22⋊D19111yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—3822no—
176Q8—3822no—
177D4—24no—
178D4—42no—
179D4—3822no—
180D4—3822no—
181D4—7644no—
182D4—7644no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—3822no—
187C2×C4—7644no—
188C2×C4D4×D19114yes—
189C2×C4C2×C22⋊D19112yes—
190C2×C4C2×C22⋊D19112yes—
191C2×C4C2×C22⋊D19111yescharacteristic
192C2×C4C23×D19111yescharacteristic
193C8—1918no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—7642no—
199C22—7644no—
200C22#2025931812yes—
201C22C22×C22⋊D19111yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—7642no—
206C4#2025931812yes—
207C4C2×D4×D19112yes—
208C2—22no—
209C2—82no—
210C2—15282no—
211C2C2×#2025931811yescharacteristic
212C2#2713346112yes—
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×#124×C191C2
socleC22×C191C22×D4
hypercenterC2×#124D191
hypocenterC191#3153
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#20259353C2semidirect
2. C2×#20259348C2semidirect
3. #27133213C2semidirect
4. #27133058C2semidirect
5. #27133053C2semidirect
6. #27133045C2semidirect
7. C4×#15690271C2semidirect
8. C2×#124×C191C2semidirect
12. C2×#15690277C22semidirect
14. C2×#15690274C22semidirect
17. #20259322C22semidirect
18. #20259319C22semidirect
19. #20259310C22semidirect
22. #20259233C22semidirect
23. C4×C191⋊C8C22semidirect
42. #15690271D4semidirect
106. C191#3153semidirect
111. C2×#124D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593532
C2×#202593482
#271332132
#271330582
#271330532
#271330452
C4×#156902712
C2×#124×C1912
#3153191