Finite Group Databasebeta

← #35303860

Subgroups — #35303860

Order 21248.

414 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19128104C211yesmaximal, characteristic
2#24907634C211yesmaximal, characteristic
3#24906149C211yesmaximal, characteristic
4#24906148C211yesmaximal, characteristic
5#24906143C211yesmaximal, characteristic
6#24905747C211yesmaximal, characteristic
7C83×#1548C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9#19128104—21no—
10#19128104—21no—
11#19128104C414yes—
12#19127754C2211yescharacteristic
13C2×#14581727—22no—
14C2×#14581725—22no—
15#19127725C2211yescharacteristic
16C2×C4×C83⋊C8C2211yescharacteristic
17#19127449—22no—
18#19127447—22no—
19#19127446—22no—
20#19127423—21no—
21C8×C83⋊C8—21no—
22C2×C4⋊Q8×C83C2211yescharacteristic
23#431×C83C2211yescharacteristic
24#423×C83C2211yescharacteristic
25#333×C83—22no—
26C22×Dic166—21no—
27C2×#13050574—21no—
28C22×C83⋊C8D412yes—
29#14581792—21no—
30#14581792—21no—
31#14581792—21no—
32#14581792C2×C412yes—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83—21no—
35#14581727—44no—
36#14581725—24no—
37#14581725—24no—
38C4⋊(C83⋊C8)—21no—
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)D412yes—
41C22⋊(C83⋊C8)—21no—
42C4×C83⋊C8—21no—
43C4×C83⋊C8C2×C412yes—
44C4×C83⋊C8D411yescharacteristic
45C4×C83⋊C8D411yescharacteristic
46C22×Q8×C83—21no—
47C2×M16×C83—21no—
48C4⋊Q8×C83—21no—
49C4⋊Q8×C83—21no—
50C4⋊Q8×C83—21no—
51C4⋊Q8×C83C2×C412yes—
52C2×C4⋊C4×C83—21no—
53C2×C4⋊C4×C83—21no—
54C2×C42×C83C2311yescharacteristic
55C4⋊C8×C83—21no—
56C4⋊C8×C83—21no—
57C4⋊C8×C83D412yes—
58C22⋊C8×C83—21no—
59C4×C8×C83—21no—
60C2×Dic166—22no—
61C2×Dic166—41no—
62C2×Dic166—82no—
63C22×Dic83—41no—
64#13050574—42no—
65C2×C83⋊C8—22no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8C22⋊C412yes—
68C2×C83⋊C8C22⋊C412yes—
69C2×C83⋊C8SD1614yes—
70C2×C83⋊C8Q1614yes—
71C4⋊Dic83—22no—
72C4⋊Dic83—22no—
73C4⋊Dic83—41no—
74C4⋊Dic83—41no—
75C2×Q8×C83—22no—
76C2×Q8×C83—41no—
77C2×Q8×C83—82no—
78C22×C4×C83—41no—
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83#4111yescharacteristic
81C22×C4×C83#4111yescharacteristic
82M16×C83—42no—
83C2×C8×C83—22no—
84C2×C8×C83—41no—
85C4⋊C4×C83—22no—
86C4⋊C4×C83—22no—
87C4⋊C4×C83—41no—
88C4⋊C4×C83—41no—
89C42×C83C22×C411yescharacteristic
90C42×C83C2×D411yescharacteristic
91C42×C83C2×D411yescharacteristic
92C42×C83C2×D411yescharacteristic
93C23×C83#12411yescharacteristic
94Q8×C83—82no—
95Q8×C83—82no—
96C2×C4×C83—22no—
97C2×C4×C83—22no—
98C2×C4×C83—42no—
99C2×C4×C83—82no—
100C2×C4×C83C2×C22⋊C411yescharacteristic
101C2×C4×C83C4×D411yescharacteristic
102C2×C4×C83C4×D411yescharacteristic
103C2×C4×C83#12111yescharacteristic
104C2×C4×C83#12111yescharacteristic
105C2×C4×C83#12711yescharacteristic
106C2×C4×C83C2×SD1612yes—
107C2×C4×C83C2×Q1612yes—
108C2×Dic83—42no—
109C2×Dic83—82no—
110Dic166—82no—
111Dic166—82no—
112C8×C83—42no—
113C8×C83—81no—
114C83⋊C8—42no—
115C83⋊C8—81no—
116C83⋊C8#10314yes—
117C83⋊C8#10314yes—
118C22×C83—21no—
119C22×C83—21no—
120C22×C83#39011yescharacteristic
121C22×C83#48712yes—
122C4×C83—21no—
123C4×C83—21no—
124C4×C83—82no—
125C4×C83C2×#10312yes—
126C4×C83#47212yes—
127C4×C83#47312yes—
128C4×C83#49211yescharacteristic
129C4×C83#49411yescharacteristic
130Dic83—82no—
131#9771—831nomaximal, Sylow
132C2×C83—22no—
133C2×C83#195611yescharacteristic
134C2×C83#197811yescharacteristic
135C2×C83#197911yescharacteristic
136C2×#500—831no—
137#1848—831no—
138#1549—831no—
139#1549—831no—
140#1548—831no—
141#1548D8311yescharacteristic
142#1450—831no—
143C83#977111yescharacteristic, complemented, Sylow
144C2×C4⋊Q8—831no—
145C2×C4⋊Q8C2×D8311yescharacteristic
146#500—834no—
147#500—1661no—
148#500—1661no—
149#431—831no—
150#431C2×D8311yescharacteristic
151C2×#108—1662no—
152C2×#107—1662no—
153#423—831no—
154#423C2×D8311yescharacteristic
155C2×C4×C8—831no—
156#333—22no—
157#333—1662no—
158#332—1662no—
159#332—1662no—
160#322—1661no—
161C82—1661no—
162C22×Q8—21no—
163C22×Q8—1661no—
164C2×M16—21no—
165C2×M16—1661no—
166C22×C8—832no—
167C4⋊Q8—21no—
168C4⋊Q8—21no—
169C4⋊Q8—21no—
170C4⋊Q8—832no—
171C4⋊Q8—1661no—
172C4⋊Q8—1661no—
173C4⋊Q8—1661no—
174C4⋊Q8C4×D8312yes—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—1661no—
178C2×C4⋊C4—1661no—
179C2×C42C22×D8311yescharacteristic
180#108—3324no—
181#107—1664no—
182#107—1664no—
183C4⋊C8—21no—
184C4⋊C8—21no—
185C4⋊C8—832no—
186C4⋊C8—1661no—
187C4⋊C8—1661no—
188C4⋊C8C22⋊D8312yes—
189C22⋊C8—21no—
190C22⋊C8—1661no—
191C4×C8—21no—
192C4×C8—832no—
193C4×C8—831no—
194C4×C8—831no—
195C4×C8—1661no—
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—82no—
199C2×Q8—3321no—
200C2×Q8—6642no—
201C2×Q8—1662no—
202C22×C4—41no—
203C22×C4—3321no—
204C22×C4D4×D8311yescharacteristic
205C22×C4#1305058911yescharacteristic
206C22×C4#1305059011yescharacteristic
207M16—42no—
208M16—3322no—
209C2×C8—22no—
210C2×C8—41no—
211C2×C8—3321no—
212C2×C8—834no—
213C2×C8—834no—
214C2×C8—832no—
215C2×C8—832no—
216C2×C8—1662no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—3321no—
222C4⋊C4—3321no—
223C4⋊C4—1662no—
224C4⋊C4—1662no—
225C42C2×C4×D8311yescharacteristic
226C42D4×D8311yescharacteristic
227C42D4×D8311yescharacteristic
228C42C2×C22⋊D8311yescharacteristic
229C23#1458177811yescharacteristic
230Q8—82no—
231Q8—82no—
232Q8—6642no—
233Q8—6642no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—42no—
237C2×C4—82no—
238C2×C4—3322no—
239C2×C4—6642no—
240C2×C4C22⋊C4×D8311yescharacteristic
241C2×C4(C22⋊D83)⋊C411yescharacteristic
242C2×C4C4×C22⋊D8311yescharacteristic
243C2×C4#1458176411yescharacteristic
244C2×C4#1458176511yescharacteristic
245C2×C4#1458178811yescharacteristic
246C2×C4SD16×D8312yes—
247C2×C4Q16×D8312yes—
248C8—42no—
249C8—81no—
250C8—3322no—
251C8—834no—
252C8—834no—
253C8—6641no—
254C22—21no—
255C22—21no—
256C22#1912760111yescharacteristic
257C22#1912805012yes—
258C4—21no—
259C4—21no—
260C4—82no—
261C4—6642no—
262C4#103×D8312yes—
263C4#1912797012yes—
264C4#1912797412yes—
265C4#1912807211yescharacteristic
266C4#1912807911yescharacteristic
267C2—22no—
268C2#2490826311yescharacteristic
269C2#2490837011yescharacteristic
270C2#2490837711yescharacteristic
subgroupG/H
centerC22#19127601
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1548C2
socleC22×C83#390
prime radicalC23×C83#124
cosocleC2×C42×C83C23
hypercenter#1548D83
hypocenterC83#9771
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
143. C83#9771semidirect

Maximal subgroups

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

subgroupindex
C2×#191281042
#249076342
#249061492
#249061482
#249061432
#249057472
C83×#15482
#977183