Finite Group Databasebeta

← #35313845

Subgroups — #35313845

Order 21248.

288 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 69 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#24916103C211yesmaximal, characteristic
2#24909272C212yesmaximal, complemented
3#24905415C212yesmaximal, complemented
4#24905401C211yesmaximal, characteristic
5C83×#1321C211yesmaximal, characteristic
6#41×Dic83C411yescharacteristic
7#19127759—22no—
8#19127751—22no—
9#19127729C2211yescharacteristic
10#19127727C411yescharacteristic
11#19127668C411yescharacteristic
12M16×Dic83C2211yescharacteristic
13C2×C8×Dic83C411yescharacteristic
14#19127521—22no—
15#19127483C2212yes—
16#19127478—22no—
17#408×C83C2211yescharacteristic
18#349×C83C2212yes—
19C2×#13050574C2×C411yescharacteristic
20C22×C83⋊C8C2×C411yescharacteristic
21Q8×Dic83—21no—
22D4×Dic83—22no—
23D4×Dic83—21no—
24#14581751—21no—
25#14581751C2×C411yescharacteristic
26C2×C4×Dic83—21no—
27C2×C4×Dic83C2×C411yescharacteristic
28#14581732—22no—
29Dic83⋊C8—22no—
30Dic83⋊C8—22no—
31C22⋊(C83⋊C8)—22no—
32#14581702D412yes—
33C8×Dic83—21no—
34C8×Dic83—21no—
35C8×Dic83D412yes—
36C2×#41×C83C2×C411yescharacteristic
37C2×M16×C83C2311yescharacteristic
38C22×C8×C83C2×C411yescharacteristic
39M32×C83—22no—
40C22⋊C8×C83—22no—
41C22×Dic83—22no—
42C22×Dic83—21no—
43#13050574—41no—
44C2×C83⋊C8—21no—
45C2×C83⋊C8—41no—
46C2×C83⋊C8C22⋊C412yes—
47C4⋊Dic83—22no—
48C4⋊Dic83—21no—
49C22⋊Dic83—22no—
50C22⋊Dic83M1612yes—
51C4×Dic83—22no—
52C4×Dic83—21no—
53C4×Dic83—21no—
54C4×Dic83C22⋊C411yescharacteristic
55C4×Dic83C22⋊C411yescharacteristic
56C83⋊C16—42no—
57#41×C83—41no—
58#41×C83—41no—
59C2×Q8×C83M1611yescharacteristic
60C2×D4×C83—21no—
61C2×D4×C83M1611yescharacteristic
62C22×C4×C83—21no—
63C22×C4×C83C22×C411yescharacteristic
64M16×C83—41no—
65C2×C8×C83—21no—
66C2×C8×C83—41no—
67C2×C8×C83C2×D412yes—
68C16×C83—42no—
69C23×C83—21no—
70C23×C83C2×M1611yescharacteristic
71Q8×C83—41no—
72D4×C83—41no—
73D4×C83—42no—
74C2×C4×C83—21no—
75C2×C4×C83—21no—
76C2×C4×C83—21no—
77C2×C4×C83—41no—
78C2×C4×C83—41no—
79C2×C4×C83C2×C22⋊C411yescharacteristic
80C2×C4×C83C2×M1611yescharacteristic
81C2×Dic83—21no—
82C2×Dic83—22no—
83C2×Dic83—21no—
84C2×Dic83—42no—
85C2×Dic83—44no—
86C8×C83—22no—
87C8×C83—41no—
88C83⋊C8—22no—
89C83⋊C8—41no—
90C22×C83—21no—
91C22×C83—41no—
92C22×C83—42no—
93C22×C83—41no—
94C22×C83#40711yescharacteristic
95C4×C83—21no—
96C4×C83—41no—
97C4×C83#41011yescharacteristic
98C4×C83#41311yescharacteristic
99Dic83—22no—
100Dic83—42no—
101Dic83—41no—
102#11524—831nomaximal, Sylow
103C2×C83—21no—
104C2×C83—41no—
105C2×C83—81no—
106C2×C83#146411yescharacteristic
107#2922—831no—
108#2165—832no—
109#1328—832no—
110#1321—831no—
111#1321D8311yescharacteristic
112C83#1152411yescharacteristic, complemented, Sylow
113C4×#41—831no—
114#433—1662no—
115#431—1662no—
116#424—831no—
117#424—831no—
118#408—831no—
119#408C2×D8311yescharacteristic
120C4×M16—831no—
121C2×C4×C8—831no—
122#364—1662no—
123#349—832no—
124#349C2×D8312yes—
125#347—1662no—
126C2×#41C4×D8311yescharacteristic
127C2×M16—831no—
128C2×M16C22×D8311yescharacteristic
129C22×C8—831no—
130C22×C8C4×D8311yescharacteristic
131C4×Q8—1661no—
132C4×D4—1662no—
133C4×D4—1661no—
134#117—831no—
135#117—1661no—
136C2×C42—831no—
137C2×C42—1661no—
138M32—22no—
139M32—1662no—
140C4⋊C8—1662no—
141C4⋊C8—1662no—
142C22⋊C8—22no—
143C22⋊C8—1662no—
144#97—832no—
145C4×C8—832no—
146C4×C8—1661no—
147C4×C8—1661no—
148#41—41no—
149#41—41no—
150C2×Q8#1305057311yescharacteristic
151C2×D4—21no—
152C2×D4#1305057311yescharacteristic
153C22×C4—21no—
154C22×C4—1662no—
155C22×C4—1661no—
156C22×C4C2×C4×D8311yescharacteristic
157M16—41no—
158M16—3321no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—3321no—
162C2×C8—832no—
163C2×C8—1661no—
164C2×C8D4×D8312yes—
165C4⋊C4—1662no—
166C4⋊C4—1661no—
167C22⋊C4—832no—
168C22⋊C4—1662no—
169C42—831no—
170C42—831no—
171C42—1662no—
172C42—1661no—
173C42—1661no—
174C16—42no—
175C16—3322no—
176C23—21no—
177C23M16×D8311yescharacteristic
178Q8—41no—
179D4—41no—
180D4—42no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—3322no—
187C2×C4—3324no—
188C2×C4—1661no—
189C2×C4—1662no—
190C2×C4—1661no—
191C2×C4C22⋊C4×D8311yescharacteristic
192C2×C4C2×#1305057311yescharacteristic
193C8—22no—
194C8—41no—
195C8—3321no—
196C8—1662no—
197C22—21no—
198C22—41no—
199C22—42no—
200C22—41no—
201C22#1912766311yescharacteristic
202C4—21no—
203C4—41no—
204C4—3321no—
205C4—3322no—
206C4—1662no—
207C4#1912767311yescharacteristic
208C4#1912768211yescharacteristic
209C2—21no—
210C2—41no—
211C2—81no—
212C2#2490579411yescharacteristic
subgroupG/H
centerC4#19127673
commutatorC22×C4×C83C22×C4
FrattiniC2×M16C22×D83
FittingC83×#1321C2
socleC2×C83#1464
prime radicalC2×#41×C83C2×C4
cosocleC2×M16×C83C23
hypercenter#1321D83
hypocenterC83#11524
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #24909272C2semidirect
3. #24905415C2semidirect
112. C83#11524semidirect

Maximal subgroups

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

subgroupindex
#249161032
#249092722
#249054152
#249054012
C83×#13212
#1152483