Finite Group Databasebeta

← #24909146

Subgroups — #24909146

Order 10624.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#19128247C211yesmaximal, characteristic
2#19127685C211yesmaximal, characteristic, complemented
3#19127499C212yesmaximal, complemented
4#19127497C212yesmaximal, complemented
5#413×C83C211yesmaximal, characteristic, complemented
6C2×#13050590C411yescharacteristic
7C2×#13050574—21no—
8#14581790C2211yescharacteristic
9#14581788C411yescharacteristic
10#14581781C2211yescharacteristic
11#14581779C411yescharacteristic
12#14581764—21no—
13#14581764—21no—
14C4×C22⋊D83—21no—
15C4×C22⋊D83—21no—
16C2×C4×Dic83C411yescharacteristic
17#14581711C2212yes—
18#14581709—21no—
19C2×#41×C83C2211yescharacteristic
20C2×M16×C83—21no—
21#101×C83C2212yes—
22#100×C83—21no—
23#13050590—41no—
24#13050590—41no—
25C2×Dic166C2×C411yescharacteristic
26C2×D332C2×C411yescharacteristic
27C2×C22⋊D83—21no—
28C2×C22⋊D83—21no—
29C2×C22⋊D83—21no—
30C22×Dic83—21no—
31C2×C4×D83—21no—
32#13050574—22no—
33#13050574—41no—
34C2×C83⋊C8—41no—
35Dic83⋊C4—21no—
36Dic83⋊C4—21no—
37C22⋊Dic83—21no—
38C22⋊Dic83—21no—
39(C2×D83)⋊C4—21no—
40(C2×D83)⋊C4—21no—
41C4×Dic83—21no—
42C4×Dic83C2×C411yescharacteristic
43C4×Dic83C2×C411yescharacteristic
44#41×C83—41no—
45#41×C83—41no—
46C2×Q8×C83C2311yescharacteristic
47C2×D4×C83C2×C411yescharacteristic
48C2×D4×C83D411yescharacteristic
49C2×D4×C83D411yescharacteristic
50C22×C4×C83C2×C411yescharacteristic
51C22×C4×C83D411yescharacteristic
52C22×C4×C83D411yescharacteristic
53M16×C83—22no—
54M16×C83—41no—
55C2×C8×C83—41no—
56C23×C83C22⋊C411yescharacteristic
57C23×C83C22⋊C411yescharacteristic
58C23×C83C22⋊C411yescharacteristic
59C22×D83—21no—
60Q8×C83—41no—
61D4×C83—41no—
62D4×C83—41no—
63D4×C83—41no—
64C2×C4×C83—21no—
65C2×C4×C83—21no—
66C2×C4×C83—21no—
67C2×C4×C83—21no—
68C2×C4×C83—21no—
69C2×C4×C83—21no—
70C2×C4×C83C22⋊C411yescharacteristic
71C2×C4×C83C22×C411yescharacteristic
72C2×C4×C83C2×D411yescharacteristic
73C2×C4×C83C2×D411yescharacteristic
74C22⋊D83—42no—
75C22⋊D83—42no—
76C22⋊D83—42no—
77C2×Dic83—21no—
78C2×Dic83—21no—
79C2×Dic83—21no—
80C2×Dic83—42no—
81D332—41no—
82C4×D83—41no—
83C4×D83—41no—
84Dic166—41no—
85C8×C83—42no—
86C83⋊C8—42no—
87C22×C83—21no—
88C22×C83—21no—
89C22×C83—21no—
90C22×C83—41no—
91C22×C83—41no—
92C22×C83—41no—
93C22×C83C2×C22⋊C411yescharacteristic
94C2×D83—41no—
95C2×D83—41no—
96C2×D83—41no—
97C4×C83—21no—
98C4×C83—21no—
99C4×C83—21no—
100C4×C83#9911yescharacteristic
101C4×C83#9911yescharacteristic
102Dic83—22no—
103Dic83—41no—
104Dic83—41no—
105C2×C83—21no—
106C2×C83—41no—
107C2×C83—41no—
108C2×C83—41no—
109C2×C83C2×#9911yescharacteristic
110D83—81no—
111#2132—831nomaximal, Sylow
112C83#213211yescharacteristic, complemented, Sylow
113#532—831no—
114#413—831no—
115#413D8311yescharacteristic, complemented
116#356—832no—
117#355—832no—
118C2×#41—831no—
119C2×#41C2×D8311yescharacteristic
120C2×M16—21no—
121C2×M16—1661no—
122C4⋊Q8—831no—
123#127—831no—
124#124—831no—
125#124—831no—
126#121—1661no—
127#121—1661no—
128C4×D4—1661no—
129C4×D4—1661no—
130C2×C42—831no—
131#101—832no—
132#101C2×D8312yes—
133#100—21no—
134#100—1661no—
135#41—41no—
136#41—41no—
137#41—3321no—
138#41—3321no—
139C2×Q8—831no—
140C2×Q8C22×D8311yescharacteristic
141C2×D4—831no—
142C2×D4—1661no—
143C2×D4—1661no—
144C2×D4—1661no—
145C2×D4C4×D8311yescharacteristic
146C2×D4D33211yescharacteristic
147C2×D4C22⋊D8311yescharacteristic
148C22×C4—1661no—
149C22×C4—1661no—
150C22×C4C4×D8311yescharacteristic
151C22×C4D33211yescharacteristic
152C22×C4C22⋊D8311yescharacteristic
153M16—22no—
154M16—41no—
155M16—3321no—
156M16—1662no—
157C2×C8—41no—
158C2×C8—3321no—
159C4⋊C4—1661no—
160C4⋊C4—1661no—
161C22⋊C4—1661no—
162C22⋊C4—1661no—
163C22⋊C4—1661no—
164C22⋊C4—1661no—
165C42—831no—
166C42—831no—
167C42—1661no—
168C23—1661no—
169C23(C2×D83)⋊C411yescharacteristic
170C23(C2×D83)⋊C411yescharacteristic
171C23(C2×D83)⋊C411yescharacteristic
172Q8—41no—
173Q8—3321no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—3321no—
178D4—3322no—
179D4—3322no—
180D4—3322no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—3322no—
188C2×C4—3321no—
189C2×C4—3321no—
190C2×C4—1661no—
191C2×C4—1661no—
192C2×C4—1661no—
193C2×C4(C2×D83)⋊C411yescharacteristic
194C2×C4C2×C4×D8311yescharacteristic
195C2×C4C2×C22⋊D8311yescharacteristic
196C2×C4C2×D33211yescharacteristic
197C8—42no—
198C8—3322no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—3321no—
206C22—3321no—
207C22—3321no—
208C22C2×(C2×D83)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—3321no—
213C4—3321no—
214C4—1662no—
215C4#1458170611yescharacteristic
216C4#1458170611yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—6641no—
222C2C2×#1458170611yescharacteristic
subgroupG/H
centerC4#14581706
commutatorC2×C4×C83C22×C4
FrattiniC2×Q8C22×D83
Fitting#413×C83C2
socleC2×C83C2×#99
prime radical#19128247C2
cosocleC2×Q8×C83C23
hypercenter#413D83
hypocenterC83#2132
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #19127685C2semidirect
3. #19127499C2semidirect
4. #19127497C2semidirect
5. #413×C83C2semidirect
112. C83#2132semidirect
115. #413D83semidirect

Maximal subgroups

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

subgroupindex
#191282472
#191276852
#191274992
#191274972
#413×C832
#213283