Finite Group Databasebeta

← #35308044

Subgroups — #35308044

Order 21248.

376 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 101 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#24907459C211yesmaximal, characteristic
2#24906237C211yesmaximal, characteristic
3#24906148C211yesmaximal, characteristic
4#24906144C211yesmaximal, characteristic
5#24905858C211yesmaximal, characteristic
6#24905360C211yesmaximal, characteristic
7C2×#475×C83C211yesmaximal, characteristic
8#19127754C2211yescharacteristic
9#19127754C2211yescharacteristic
10#19127725C2211yescharacteristic
11#19127725C2211yescharacteristic
12C2×#14581711—21no—
13#19127470—21no—
14#19127453—22no—
15#19127450—22no—
16#19127447—22no—
17Q8⋊(C83⋊C8)—22no—
18C2×C4⋊Q8×C83C2211yescharacteristic
19C2×C4×Q8×C83C2211yescharacteristic
20#475×C83—22no—
21#475×C83—22no—
22C2×#106×C83—21no—
23C2×C4⋊C8×C83C2211yescharacteristic
24C2×#103×C83—21no—
25C2×#13050574—21no—
26C2×#13050574—21no—
27C4⋊(C83⋊C8)—21no—
28C4⋊(C83⋊C8)—21no—
29C4⋊(C83⋊C8)—21no—
30C4⋊(C83⋊C8)—21no—
31C4⋊(C83⋊C8)—21no—
32C4⋊(C83⋊C8)D412yes—
33#14581711—42no—
34C22⋊(C83⋊C8)—21no—
35C22⋊(C83⋊C8)—21no—
36C4×C83⋊C8—21no—
37C4×C83⋊C8—21no—
38C22×Q8×C83—21no—
39C22×Q8×C83D411yescharacteristic
40C22×C8×C83—21no—
41C4⋊Q8×C83—21no—
42C4⋊Q8×C83—21no—
43C4⋊Q8×C83—21no—
44C4⋊Q8×C83D412yes—
45C4×Q8×C83—21no—
46C4×Q8×C83—21no—
47C4×Q8×C83—21no—
48C4×Q8×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83—21no—
52C2×C4⋊C4×C83D411yescharacteristic
53C2×C42×C83—21no—
54C2×C42×C83C2311yescharacteristic
55#106×C83—24no—
56C4⋊C8×C83—21no—
57C4⋊C8×C83D412yes—
58#103×C83—24no—
59#13050574—41no—
60#13050574—41no—
61#13050574—41no—
62#13050574—41no—
63C2×C83⋊C8—22no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×Q8×C83—21no—
68C2×Q8×C83—21no—
69C2×Q8×C83—21no—
70C2×Q8×C83—22no—
71C2×Q8×C83—21no—
72C2×Q8×C83—21no—
73C2×Q8×C83—41no—
74C2×Q8×C83—82no—
75C2×Q8×C83Q1612yes—
76C22×C4×C83—21no—
77C22×C4×C83—21no—
78C22×C4×C83—41no—
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83#4111yescharacteristic
81C22×C4×C83#4111yescharacteristic
82C2×C8×C83—22no—
83C2×C8×C83—41no—
84C2×C8×C83—41no—
85C4⋊C4×C83—22no—
86C4⋊C4×C83—21no—
87C4⋊C4×C83—22no—
88C4⋊C4×C83—21no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C4⋊C4×C83—41no—
93C42×C83—41no—
94C42×C83—41no—
95C42×C83C2×D411yescharacteristic
96C42×C83C2×D411yescharacteristic
97C42×C83C2×D411yescharacteristic
98C42×C83#4111yescharacteristic
99C23×C83#12311yescharacteristic
100Q8×C83—22no—
101Q8×C83—22no—
102Q8×C83—41no—
103Q8×C83—41no—
104Q8×C83—82no—
105Q8×C83—82no—
106C2×C4×C83—22no—
107C2×C4×C83—22no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—42no—
113C2×C4×C83—82no—
114C2×C4×C83—81no—
115C2×C4×C83#12011yescharacteristic
116C2×C4×C83#12111yescharacteristic
117C2×C4×C83#12111yescharacteristic
118C2×C4×C83#12111yescharacteristic
119C2×C4×C83#12311yescharacteristic
120C2×C4×C83#12411yescharacteristic
121C2×C4×C83C2×Q1611yescharacteristic
122C2×C4×C83#13511yescharacteristic
123C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C83#13711yescharacteristic
125C8×C83—42no—
126C83⋊C8—42no—
127C83⋊C8—81no—
128C83⋊C8—81no—
129C83⋊C8—81no—
130C22×C83—21no—
131C22×C83—21no—
132C22×C83#39411yescharacteristic
133C22×C83#48411yescharacteristic
134C22×C83#48511yescharacteristic
135C4×C83—21no—
136C4×C83—21no—
137C4×C83—21no—
138C4×C83—42no—
139C4×C83—81no—
140C4×C83—82no—
141C4×C83#44911yescharacteristic
142C4×C83#45111yescharacteristic
143C4×C83#46711yescharacteristic
144C4×C83#46811yescharacteristic
145C4×C83#47112yes—
146#10451—831nomaximal, Sylow
147C2×C83—21no—
148C2×C83—21no—
149C2×C83#203611yescharacteristic
150C2×C83#204611yescharacteristic
151C2×C83#204911yescharacteristic
152C2×#475D8311yescharacteristic
153#1801—831no—
154#1571—831no—
155#1549—831no—
156#1548—831no—
157#1479—831no—
158#1301—831no—
159C83#1045111yescharacteristic, complemented, Sylow
160C2×C4⋊Q8C2×D8311yescharacteristic
161C2×C4×Q8C2×D8311yescharacteristic
162#475—22no—
163#475—22no—
164#431—831no—
165#431—831no—
166C2×#106—21no—
167#423—831no—
168#423—831no—
169C2×C4⋊C8C2×D8311yescharacteristic
170C2×#103—21no—
171C2×#101—1661no—
172#343—1661no—
173#335—1662no—
174#333—1662no—
175#332—1662no—
176Q8⋊C8—1662no—
177C22×Q8—21no—
178C22×Q8C22⋊D8311yescharacteristic
179C2×M16—1661no—
180C2×M16—1661no—
181C22×C8—21no—
182C4⋊Q8—21no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8C22⋊D8312yes—
186C4×Q8—21no—
187C4×Q8—21no—
188C4×Q8—21no—
189C4×Q8—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C22⋊D8311yescharacteristic
194C2×C42—21no—
195C2×C42C22×D8311yescharacteristic
196#106—24no—
197C4⋊C8—21no—
198C4⋊C8—832no—
199C4⋊C8—1661no—
200C4⋊C8—1661no—
201C4⋊C8—1661no—
202C4⋊C8—1661no—
203C4⋊C8—1661no—
204C4⋊C8C22⋊D8312yes—
205#103—24no—
206#101—3322no—
207C22⋊C8—1661no—
208C22⋊C8—1661no—
209C4×C8—1661no—
210C4×C8—1661no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—22no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—41no—
218C2×Q8—82no—
219C2×Q8#1305058012yes—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4C2×C22⋊D8311yescharacteristic
224C22×C4#1305058911yescharacteristic
225C22×C4#1305058911yescharacteristic
226M16—3321no—
227M16—3321no—
228M16—3321no—
229M16—3321no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—3321no—
234C2×C8—3321no—
235C2×C8—3321no—
236C2×C8—1662no—
237C4⋊C4—22no—
238C4⋊C4—21no—
239C4⋊C4—22no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C42—41no—
246C42—41no—
247C42D4×D8311yescharacteristic
248C42C2×C22⋊D8311yescharacteristic
249C42C2×C22⋊D8311yescharacteristic
250C42#1305058911yescharacteristic
251C23#1458177311yescharacteristic
252Q8—22no—
253Q8—22no—
254Q8—41no—
255Q8—41no—
256Q8—82no—
257Q8—82no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4#1458176111yescharacteristic
268C2×C4#1458176311yescharacteristic
269C2×C4#1458176411yescharacteristic
270C2×C4#1458176411yescharacteristic
271C2×C4#1458177311yescharacteristic
272C2×C4#1458177911yescharacteristic
273C2×C4C2×#1305058011yescharacteristic
274C2×C4#1458181211yescharacteristic
275C2×C4#1458181711yescharacteristic
276C2×C4#1458182311yescharacteristic
277C8—42no—
278C8—3322no—
279C8—6641no—
280C8—6641no—
281C8—6641no—
282C22—21no—
283C22—21no—
284C22#1912761511yescharacteristic
285C22#1912803411yescharacteristic
286C22#1912803911yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—42no—
291C4—82no—
292C4—81no—
293C4#1912784611yescharacteristic
294C4#1912785711yescharacteristic
295C4#1912794011yescharacteristic
296C4#1912794911yescharacteristic
297C4#1912796112yes—
298C2—21no—
299C2—21no—
300C2#2490866311yescharacteristic
301C2#2490872111yescharacteristic
302C2#2490874011yescharacteristic
subgroupG/H
centerC22#19127615
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC2×#475×C83C2
socleC22×C83#394
prime radicalC23×C83#123
hypercenterC2×#475D83
hypocenterC83#10451
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
159. C83#10451semidirect

Maximal subgroups

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

subgroupindex
#249074592
#249062372
#249061482
#249061442
#249058582
#249053602
C2×#475×C832
#1045183