Finite Group Databasebeta

← #35307089

Subgroups — #35307089

Order 21248.

614 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 111 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#24918581C212yesmaximal
2#24915861C211yesmaximal, characteristic, complemented
3#24906136C212yesmaximal, complemented
4#24905296C211yesmaximal, characteristic, complemented
5C83×#1962C211yesmaximal, characteristic
6C2×#14581792—22no—
7C2×#14581792C2212yes—
8#19128104—22no—
9#19128047—22no—
10#19128012—24no—
11#19127981—24no—
12#19127754C2212yes—
13#19127571—24no—
14#19127448—24no—
15#532×C83C2211yescharacteristic
16#423×C83C2211yescharacteristic
17C2×#104×C83—22no—
18C43×C83C2211yescharacteristic
19C22×Dic166—22no—
20#14581792—22no—
21#14581792—22no—
22#14581792—22no—
23#14581792—22no—
24#14581792—44no—
25#14581792—44no—
26C2×C4⋊Dic83—28no—
27C2×C4⋊Dic83—22no—
28C2×C4⋊Dic83D414yes—
29#14581725—28no—
30C4⋊(C83⋊C8)D414yes—
31#14581713—28no—
32C22⋊(C83⋊C8)—22no—
33C4×C83⋊C8—22no—
34C2×#41×C83—21no—
35C2×M16×C83—21no—
36C4⋊Q8×C83D411yescharacteristic
37#127×C83D411yescharacteristic
38#124×C83—21no—
39#121×C83—22no—
40C4×D4×C83—22no—
41C2×C42×C83—22no—
42C2×C42×C83D412yes—
43C2×C42×C83C2311yescharacteristic
44C4⋊C8×C83—22no—
45#104×C83—44no—
46C2×Dic166—42no—
47C2×Dic166—42no—
48C2×Dic166—44no—
49C2×Dic166—44no—
50C22×Dic83—24no—
51C2×C83⋊C8—24no—
52C4⋊Dic83—24no—
53C4⋊Dic83—24no—
54C4⋊Dic83—416no—
55C4⋊Dic83—42no—
56C4⋊Dic83—42no—
57#41×C83—42no—
58#41×C83—42no—
59C2×Q8×C83—21no—
60C2×D4×C83—22no—
61C2×D4×C83—21no—
62C2×D4×C83—41no—
63C22×C4×C83—22no—
64C22×C4×C83—41no—
65C22×C4×C83C2×D412yes—
66C22×C4×C83C2×D411yescharacteristic
67M16×C83—42no—
68C2×C8×C83—41no—
69C4⋊C4×C83—22no—
70C22⋊C4×C83—42no—
71C42×C83—28no—
72C42×C83—22no—
73C42×C83D814yes—
74C42×C83C2×D412yes—
75C42×C83C2×D411yescharacteristic
76C42×C83#4111yescharacteristic
77C23×C83—41no—
78C23×C83#12011yescharacteristic
79Q8×C83—42no—
80D4×C83—44no—
81D4×C83—42no—
82D4×C83—82no—
83C2×C4×C83—28no—
84C2×C4×C83—24no—
85C2×C4×C83—24no—
86C2×C4×C83—41no—
87C2×C4×C83—81no—
88C2×C4×C83—81no—
89C2×C4×C83#12012yes—
90C2×C4×C83#12112yes—
91C2×C4×C83#12111yescharacteristic
92C2×C4×C83#12711yescharacteristic
93C2×C4×C83C2×D812yes—
94C2×C4×C83AGL(1,ℤ/8)12yes—
95C2×Dic83—44no—
96C2×Dic83—48no—
97Dic166—84no—
98Dic166—82no—
99Dic166—82no—
100C8×C83—81no—
101C83⋊C8—44no—
102C22×C83—22no—
103C22×C83—82no—
104C22×C83—81no—
105C22×C83#39211yescharacteristic
106C22×C83#44712yes—
107C4×C83—28no—
108C4×C83—22no—
109C4×C83—81no—
110C4×C83#45614yes—
111C4×C83#45912yes—
112C4×C83#49311yescharacteristic
113C4×C83#49611yescharacteristic
114Dic83—84no—
115#10289—831nomaximal, Sylow
116C2×C83—22no—
117C2×C83—161no—
118C2×C83#200512yes—
119C2×C83#201111yescharacteristic
120#3226—832no—
121#2868—831no—
122#1962D8311yescharacteristic
123#1546—832no—
124#1276—831no—
125C83#1028911yescharacteristic, complemented, Sylow
126#532C2×D8311yescharacteristic
127C2×C4⋊Q8—832no—
128C2×C4⋊Q8—1662no—
129#500—1662no—
130#486—1662no—
131#480—1664no—
132#474—1664no—
133#431—832no—
134#423C2×D8311yescharacteristic
135C2×#104—22no—
136#384—1664no—
137C43C2×D8311yescharacteristic
138#332—1664no—
139C2×#41—21no—
140C22×Q8—1662no—
141C2×M16—21no—
142C4⋊Q8—3324no—
143C4⋊Q8—3324no—
144C4⋊Q8—1662no—
145C4⋊Q8—1662no—
146C4⋊Q8—1662no—
147C4⋊Q8—1662no—
148C4⋊Q8D33211yescharacteristic
149#127D33211yescharacteristic
150#124—21no—
151#121—22no—
152C4×D4—22no—
153C2×C4⋊C4—834no—
154C2×C4⋊C4—1668no—
155C2×C4⋊C4—1662no—
156C2×C42—22no—
157C2×C42C22⋊D8312yes—
158C2×C42C22×D8311yescharacteristic
159#107—1668no—
160C4⋊C8—22no—
161C4⋊C8—834no—
162#104—44no—
163#102—1668no—
164C22⋊C8—1662no—
165C4×C8—1662no—
166#41—42no—
167#41—42no—
168C2×Q8—21no—
169C2×Q8—3322no—
170C2×Q8—3322no—
171C2×Q8—3324no—
172C2×Q8—3324no—
173C2×D4—22no—
174C2×D4—21no—
175C2×D4—41no—
176C22×C4—22no—
177C22×C4—41no—
178C22×C4—1664no—
179C22×C4D4×D8312yes—
180C22×C4C2×C22⋊D8311yescharacteristic
181M16—42no—
182C2×C8—41no—
183C2×C8—1664no—
184C4⋊C4—22no—
185C4⋊C4—33216no—
186C4⋊C4—3322no—
187C4⋊C4—3322no—
188C4⋊C4—1664no—
189C4⋊C4—1664no—
190C22⋊C4—42no—
191C42—28no—
192C42—22no—
193C42#1305057514yes—
194C42D4×D8312yes—
195C42C2×D33211yescharacteristic
196C42#1305059011yescharacteristic
197C23—41no—
198C23#1458176011yescharacteristic
199Q8—42no—
200Q8—6642no—
201Q8—6642no—
202Q8—6644no—
203D4—44no—
204D4—42no—
205D4—82no—
206C2×C4—28no—
207C2×C4—24no—
208C2×C4—24no—
209C2×C4—41no—
210C2×C4—81no—
211C2×C4—81no—
212C2×C4—3328no—
213C2×C4—3324no—
214C2×C4#1458176212yes—
215C2×C4#1458176512yes—
216C2×C4#1458176611yescharacteristic
217C2×C4#1458178811yescharacteristic
218C2×C4C2×#1305057512yes—
219C2×C4#1458181712yes—
220C8—81no—
221C8—3324no—
222C22—22no—
223C22—82no—
224C22—81no—
225C22#1912761011yescharacteristic
226C22#1912783412yes—
227C4—28no—
228C4—22no—
229C4—81no—
230C4—6644no—
231C4#1912788514yes—
232C4#1912789612yes—
233C4#1912807711yescharacteristic
234C4#1912809111yescharacteristic
235C2—22no—
236C2—161no—
237C2#2490849812yes—
238C2#2490853311yescharacteristic
subgroupG/H
centerC22#19127610
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1962C2
socleC22×C83#392
prime radical#532×C83C22
hypercenter#1962D83
hypocenterC83#10289
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
2. #24915861C2semidirect
3. #24906136C2semidirect
4. #24905296C2semidirect
125. C83#10289semidirect

Maximal subgroups

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

subgroupindex
#249185812
#249158612
#249061362
#249052962
C83×#19622
#1028983