Finite Group Databasebeta

← #37572473

Subgroups — #37572473

Order 24448.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#20259367C211yesmaximal, characteristic
2C2×#20259250C212yesmaximal, complemented
3#27132662C212yesmaximal, complemented
4C2×#20259239C211yesmaximal, characteristic, complemented
5#390×C191C211yesmaximal, characteristic, complemented
6#20259367—24no—
7#20259367—22no—
8#20259367C414yescomplemented
9C2×#15690287C2212yes—
10C2×#15690286—22no—
11C22×C22⋊D191—22no—
12C2×D4×D191—22no—
13C2×#15690271C2212yescomplemented
14#20259250—24no—
15#20259245—22no—
16#20259242—22no—
17#20259239—22no—
18C22×D4×C191C2211yescharacteristic
19C2×C4⋊C4×C191C2211yescharacteristic, complemented
20C2×C22⋊C4×C191—22no—
21C2×C42×C191C2211yescharacteristic, complemented
22C23×D191—22no—
23#15690287—22no—
24#15690287—22no—
25#15690287C2×C414yes—
26#15690287D414yes—
27#15690286—28no—
28#15690286—28no—
29C2×Dic382D412yes—
30C2×D764D412yes—
31C2×C22⋊D191—24no—
32C2×C22⋊D191—28no—
33C2×C22⋊D191—28no—
34C2×C22⋊D191—22no—
35D4×D191—28no—
36D4×D191—28no—
37C22×Dic191—22no—
38C2×C4×D191—22no—
39#15690271—22no—
40#15690271—22no—
41C2×C191⋊C8—22no—
42C24×C191D412yes—
43C2×D4×C191—22no—
44C2×D4×C191—22no—
45C2×D4×C191C2×C412yes—
46C2×D4×C191D412yes—
47C22×C4×C191—21no—
48C22×C4×C191—21no—
49C22×C4×C191C2311yescharacteristic
50C4⋊C4×C191—22no—
51C22⋊C4×C191—44no—
52C42×C191—22no—
53C22×D191—22no—
54C22×D191—28no—
55C22×D191—82no—
56C22×D191—82no—
57Dic382—22no—
58Dic382C22⋊C414yescomplemented
59D764—22no—
60D764C22⋊C414yescomplemented
61C22⋊D191—216no—
62C22⋊D191—24no—
63C22⋊D191—24no—
64C2×Dic191—28no—
65C2×Dic191—22no—
66C4×D191—24no—
67C4×D191—24no—
68C191⋊C8—42no—
69C23×C191—22no—
70C23×C191—22no—
71C23×C191—42no—
72C23×C191—42no—
73C23×C191C22⋊C414yes—
74C23×C191C2×D411yescharacteristic
75D4×C191—24no—
76D4×C191—24no—
77C2×C4×C191—22no—
78C2×C4×C191—41no—
79C2×C4×C191—41no—
80C2×C4×C191—42no—
81C2×C4×C191—41no—
82C2×C4×C191C22×C411yescharacteristic
83C2×C4×C191C2×D412yes—
84C2×C4×C191C2×D412yes—
85C2×C4×C191C2×D411yescharacteristic
86C22×C191—21no—
87C22×C191—21no—
88C22×C191—24no—
89C22×C191—44no—
90C22×C191—42no—
91C22×C191—42no—
92C22×C191—82no—
93C22×C191C2×C22⋊C411yescharacteristic
94C22×C191#12011yescharacteristic
95C22×C191#12011yescharacteristic
96C2×D191—24no—
97C2×D191—42no—
98C2×D191—42no—
99C2×D191—88no—
100C4×C191—42no—
101C4×C191—81no—
102C4×C191C2×C22⋊C412yes—
103C4×C191#12012yes—
104Dic191—24no—
105C2×C191—21no—
106C2×C191—21no—
107C2×C191—44no—
108C2×C191#37911yescharacteristic
109C2×C191#45311yescharacteristic
110C2×C191#45511yescharacteristic
111D191—44no—
112C191#179211yescharacteristic, complemented, Sylow
113#1792—1911nomaximal, Sylow
114C2×H(5,𝔽2)—1911no—
115C2×#104—1912no—
116#417—1912no—
117C2×#100—1911no—
118#390D19111yescharacteristic, complemented
119H(5,𝔽2)—3824no—
120H(5,𝔽2)—3822no—
121H(5,𝔽2)—1914no—
122C2×#41—3822no—
123C2×#41—1912no—
124C22×D4—3822no—
125C22×D4—3822no—
126C22×D4C2×D19111yescharacteristic
127C2×M16—1912no—
128C2×C4⋊C4C2×D19111yescharacteristic, complemented
129C2×C22⋊C4—22no—
130C2×C42C2×D19111yescharacteristic, complemented
131#104—3824no—
132#103—3822no—
133#102—3822no—
134#100—3822no—
135C24—3822no—
136C24C22⋊D19112yes—
137#41—3828no—
138#41—3828no—
139#41—3822no—
140#41—3822no—
141#41—1914no—
142#41—1914no—
143C2×Q8—1912no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—3828no—
147C2×D4—3828no—
148C2×D4—3824no—
149C2×D4—3828no—
150C2×D4—3828no—
151C2×D4—3822no—
152C2×D4—1912no—
153C2×D4C4×D19112yes—
154C2×D4D76412yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—3822no—
158C22×C4—3822no—
159C22×C4C22×D19111yescharacteristic
160M16—3822no—
161M16—3822no—
162C2×C8—3822no—
163C4⋊C4—22no—
164C22⋊C4—44no—
165C42—22no—
166C23—22no—
167C23—22no—
168C23—42no—
169C23—42no—
170C23—3828no—
171C23—3822no—
172C23—15282no—
173C23—15282no—
174C23(C2×D191)⋊C414yes—
175C23C2×C22⋊D19111yescharacteristic
176Q8—3822no—
177Q8—1914no—
178D4—24no—
179D4—24no—
180D4—38216no—
181D4—3824no—
182D4—3824no—
183D4—3822no—
184D4—1914no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—3828no—
191C2×C4—3822no—
192C2×C4—3824no—
193C2×C4—3824no—
194C2×C4C2×C4×D19111yescharacteristic
195C2×C4D4×D19112yes—
196C2×C4D4×D19112yes—
197C2×C4C2×D76411yescharacteristic
198C8—7642no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—44no—
203C22—42no—
204C22—42no—
205C22—82no—
206C22—3824no—
207C22—15288no—
208C22—7642no—
209C22—7642no—
210C22C2×(C2×D191)⋊C411yescharacteristic
211C22#2025929011yescharacteristic
212C22#2025929011yescharacteristic
213C4—42no—
214C4—81no—
215C4—3824no—
216C4C22⋊C4×D19112yes—
217C4#2025929212yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—7644no—
222C2#2713251811yescharacteristic
223C2#2713283011yescharacteristic
224C2#2713284011yescharacteristic
subgroupG/H
centerC22#20259290
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#390×C191C2
socleC22×C191#120
prime radicalC2×#20259367C2
cosocleC22×C4×C191C23
hypercenter#390D191
hypocenterC191#1792
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#20259250C2semidirect
3. #27132662C2semidirect
4. C2×#20259239C2semidirect
5. #390×C191C2semidirect
8. #20259367C4semidirect
13. C2×#15690271C22semidirect
19. C2×C4⋊C4×C191C22semidirect
21. C2×C42×C191C22semidirect
58. Dic382C22⋊C4semidirect
60. D764C22⋊C4semidirect
112. C191#1792semidirect
118. #390D191semidirect
128. C2×C4⋊C4C2×D191semidirect
130. C2×C42C2×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593672
C2×#202592502
#271326622
C2×#202592392
#390×C1912
#1792191