Finite Group Databasebeta

← #35304083

Subgroups — #35304083

Order 21248.

418 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 127 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#24908453C211yesmaximal, characteristic
2#24908308C211yesmaximal, characteristic
3#24906222C211yesmaximal, characteristic
4#24906144C211yesmaximal, characteristic
5#24906135C211yesmaximal, characteristic
6#24905752C211yesmaximal, characteristic
7C2×#487×C83C211yesmaximal, characteristic
8#19127754C2211yescharacteristic
9#19127725C2211yescharacteristic
10#19127725C2211yescharacteristic
11C2×#14581711—22no—
12C4×#13050574C2211yescharacteristic
13#19127470—22no—
14#19127454—22no—
15#19127450—22no—
16#19127447—22no—
17#19127423—21no—
18#19127422—21no—
19C2×C4⋊Q8×C83C2211yescharacteristic
20C2×C4⋊Q8×C83C2211yescharacteristic
21#487×C83—21no—
22#487×C83—21no—
23#487×C83—22no—
24C2×#103×C83C414yes—
25C2×C4×C8×C83C2211yescharacteristic
26C2×#13050574—21no—
27C2×#13050574—21no—
28C2×#13050574D412yes—
29C4⋊(C83⋊C8)—21no—
30C4⋊(C83⋊C8)—21no—
31C4⋊(C83⋊C8)—21no—
32C4⋊(C83⋊C8)—21no—
33C4⋊(C83⋊C8)D412yes—
34#14581711—44no—
35C22⋊(C83⋊C8)—21no—
36#14581703—21no—
37C4×C83⋊C8—21no—
38C4×C83⋊C8—21no—
39C22×Q8×C83—21no—
40C22×Q8×C83C2×C412yes—
41C22×C8×C83C2×C412yes—
42C4⋊Q8×C83—21no—
43C4⋊Q8×C83—21no—
44C4⋊Q8×C83—21no—
45C4⋊Q8×C83—21no—
46C4⋊Q8×C83—21no—
47C4⋊Q8×C83—21no—
48C4⋊Q8×C83—21no—
49C4⋊Q8×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83—21no—
52C2×C4⋊C4×C83—21no—
53C2×C4⋊C4×C83C2×C412yes—
54C2×C42×C83C2311yescharacteristic
55#103×C83—24no—
56#103×C83—24no—
57C4×C8×C83D411yescharacteristic
58C4×C8×C83D411yescharacteristic
59C4×C8×C83D412yes—
60#13050574—22no—
61#13050574—22no—
62#13050574—42no—
63#13050574—42no—
64C2×C83⋊C8—22no—
65C2×C83⋊C8—22no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8—41no—
68C2×Q8×C83—22no—
69C2×Q8×C83—22no—
70C2×Q8×C83—44no—
71C2×Q8×C83—41no—
72C2×Q8×C83—41no—
73C2×Q8×C83—42no—
74C2×Q8×C83—42no—
75C22×C4×C83—22no—
76C22×C4×C83—22no—
77C22×C4×C83C22×C411yescharacteristic
78C22×C4×C83C2×D411yescharacteristic
79C22×C4×C83#4111yescharacteristic
80C2×C8×C83—42no—
81C2×C8×C83C22⋊C412yes—
82C2×C8×C83C22⋊C412yes—
83C4⋊C4×C83—22no—
84C4⋊C4×C83—22no—
85C4⋊C4×C83—41no—
86C4⋊C4×C83—41no—
87C4⋊C4×C83—41no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—41no—
91C42×C83C2×D411yescharacteristic
92C42×C83C2×D411yescharacteristic
93C42×C83C2×D411yescharacteristic
94C42×C83#4111yescharacteristic
95C23×C83C4×D411yescharacteristic
96Q8×C83—44no—
97Q8×C83—82no—
98Q8×C83—82no—
99Q8×C83—81no—
100Q8×C83—81no—
101C2×C4×C83—22no—
102C2×C4×C83—22no—
103C2×C4×C83—42no—
104C2×C4×C83—42no—
105C2×C4×C83—44no—
106C2×C4×C83—82no—
107C2×C4×C83C2×C22⋊C411yescharacteristic
108C2×C4×C83C4×D411yescharacteristic
109C2×C4×C83#12111yescharacteristic
110C2×C4×C83#12111yescharacteristic
111C2×C4×C83#12411yescharacteristic
112C2×C4×C83#12711yescharacteristic
113C2×C4×C83AGL(1,ℤ/8)12yes—
114C2×C4×C83#13712yes—
115C8×C83—22no—
116C8×C83—22no—
117C83⋊C8—42no—
118C83⋊C8—42no—
119C83⋊C8—81no—
120C83⋊C8—81no—
121C22×C83—21no—
122C22×C83—21no—
123C22×C83#39011yescharacteristic
124C22×C83#44012yes—
125C4×C83—21no—
126C4×C83—21no—
127C4×C83—82no—
128C4×C83—82no—
129C4×C83#41312yes—
130C4×C83#46812yes—
131C4×C83#47312yes—
132C4×C83#49611yescharacteristic
133C4×C83#49711yescharacteristic
134#9809—831nomaximal, Sylow
135C2×C83—22no—
136C2×C83#196711yescharacteristic
137C2×C83#197311yescharacteristic
138C2×C83#197911yescharacteristic
139C2×#487D8311yescharacteristic
140#1997—831no—
141#1966—831no—
142#1567—831no—
143#1548—831no—
144#1546—831no—
145#1451—831no—
146C83#980911yescharacteristic, complemented, Sylow
147C2×C4⋊Q8C2×D8311yescharacteristic
148C2×C4⋊Q8C2×D8311yescharacteristic
149#487—21no—
150#487—21no—
151#487—22no—
152#431—831no—
153#423—831no—
154#423—831no—
155C2×#103Dic8314yes—
156C2×#101—1662no—
157C4×M16—831no—
158C2×C4×C8C2×D8311yescharacteristic
159#343—1662no—
160#335—1662no—
161#333—1662no—
162#332—1662no—
163#322—1661no—
164#322—1661no—
165C22×Q8—21no—
166C22×Q8C2×Dic8312yes—
167C2×M16—832no—
168C2×M16—1661no—
169C2×M16—1661no—
170C22×C8C2×Dic8312yes—
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4C2×Dic8312yes—
183C2×C42C22×D8311yescharacteristic
184C4⋊C8—832no—
185C4⋊C8—1661no—
186C4⋊C8—1661no—
187C4⋊C8—1661no—
188C4⋊C8—1661no—
189#103—24no—
190#103—24no—
191#101—3324no—
192C22⋊C8—1661no—
193#97—1661no—
194C4×C8—1661no—
195C4×C8—1661no—
196C4×C8C22⋊D8311yescharacteristic
197C4×C8C22⋊D8311yescharacteristic
198C4×C8C22⋊D8312yes—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—44no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—42no—
205C2×Q8—42no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4C22×Dic8311yescharacteristic
209C22×C4D4×D8311yescharacteristic
210C22×C4#1305058911yescharacteristic
211M16—3322no—
212M16—3322no—
213M16—1662no—
214M16—1662no—
215C2×C8—42no—
216C2×C8—3321no—
217C2×C8—3321no—
218C2×C8—1662no—
219C2×C8—1662no—
220C2×C8C22⋊Dic8312yes—
221C2×C8C22⋊Dic8312yes—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C42D4×D8311yescharacteristic
231C42C2×C22⋊D8311yescharacteristic
232C42C2×C22⋊D8311yescharacteristic
233C42#1305058911yescharacteristic
234C23D4×Dic8311yescharacteristic
235Q8—44no—
236Q8—82no—
237Q8—81no—
238Q8—81no—
239Q8—82no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—44no—
245C2×C4—82no—
246C2×C4C2×C22⋊Dic8311yescharacteristic
247C2×C4D4×Dic8311yescharacteristic
248C2×C4#1458176311yescharacteristic
249C2×C4#1458176311yescharacteristic
250C2×C4#1458177911yescharacteristic
251C2×C4#1458178811yescharacteristic
252C2×C4#1458181912yes—
253C2×C4#1458182112yes—
254C8—22no—
255C8—22no—
256C8—3322no—
257C8—3322no—
258C8—6641no—
259C8—6641no—
260C22—21no—
261C22—21no—
262C22#1912760411yescharacteristic
263C22#1912780212yes—
264C4—21no—
265C4—21no—
266C4—82no—
267C4—82no—
268C4#1912768512yes—
269C4#1912794412yes—
270C4#1912797312yes—
271C4#1912808711yescharacteristic
272C4#1912809211yescharacteristic
273C2—22no—
274C2#2490831311yescharacteristic
275C2#2490834611yescharacteristic
276C2#2490837911yescharacteristic
subgroupG/H
centerC22#19127604
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC2×#487×C83C2
socleC22×C83#390
prime radicalC23×C83C4×D4
cosocleC2×C42×C83C23
hypercenterC2×#487D83
hypocenterC83#9809
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
146. C83#9809semidirect

Maximal subgroups

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

subgroupindex
#249084532
#249083082
#249062222
#249061442
#249061352
#249057522
C2×#487×C832
#980983