Finite Group Databasebeta

← #35308187

Subgroups — #35308187

Order 21248.

366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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#24917268C211yesmaximal, characteristic
2#24906237C211yesmaximal, characteristic
3#24906121C211yesmaximal, characteristic
4#24906026C211yesmaximal, characteristic
5#24905787C211yesmaximal, characteristic
6#24905321C211yesmaximal, characteristic
7C83×#1805C211yesmaximal, characteristic
8#19128258C2211yescharacteristic
9#19128008—22no—
10#19127996—21no—
11#19127986—21no—
12#19127754C2211yescharacteristic
13#19127754C2211yescharacteristic
14#19127741—21no—
15#19127725C2211yescharacteristic
16#19127710—21no—
17#19127453—22no—
18#19127449—21no—
19#19127446—21no—
20#19127437—22no—
21#19127427—22no—
22C2×C4×Q8×C83C2211yescharacteristic
23C2×C4⋊C8×C83C2211yescharacteristic
24C2×#103×C83—21no—
25#382×C83C2211yescharacteristic
26#340×C83—21no—
27C2×#13050574—21no—
28#14581792D411yescharacteristic
29#14581792D411yescharacteristic
30#14581784—21no—
31#14581771—21no—
32#14581771—21no—
33C4×Dic166—21no—
34C4×Dic166—21no—
35#14581751—21no—
36#14581725—22no—
37#14581723—22no—
38C4⋊(C83⋊C8)—21no—
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)—21no—
41C4⋊(C83⋊C8)D412yes—
42#14581716—22no—
43#14581716—22no—
44C22⋊(C83⋊C8)—21no—
45C22⋊(C83⋊C8)D412yes—
46C4×C83⋊C8—21no—
47C4×C83⋊C8—21no—
48C22×Q8×C83D411yescharacteristic
49C22×C8×C83—21no—
50C4×Q8×C83—21no—
51C4×Q8×C83—21no—
52C4×Q8×C83—21no—
53C4×Q8×C83—21no—
54C2×C4⋊C4×C83—21no—
55C2×C4⋊C4×C83—21no—
56C2×C4⋊C4×C83D411yescharacteristic
57C2×C42×C83—21no—
58C2×C42×C83C2311yescharacteristic
59C4⋊C8×C83—21no—
60C4⋊C8×C83—21no—
61#103×C83—42no—
62#95×C83—21no—
63#95×C83—21no—
64C2×Dic166—21no—
65C2×Dic166—21no—
66#13050574—41no—
67#13050574—41no—
68C2×C83⋊C8—22no—
69C2×C83⋊C8—22no—
70C2×C83⋊C8—41no—
71C4⋊Dic83—21no—
72C4⋊Dic83—21no—
73C4⋊Dic83—21no—
74C4⋊Dic83—21no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77C22⋊Dic83—41no—
78C4×Dic83—41no—
79C2×Q8×C83—21no—
80C2×Q8×C83—21no—
81C2×Q8×C83—21no—
82C2×Q8×C83—21no—
83C2×Q8×C83—21no—
84C2×Q8×C83Q1612yes—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83—41no—
88C22×C4×C83C2×D411yescharacteristic
89C22×C4×C83C2×D411yescharacteristic
90C22×C4×C83#4111yescharacteristic
91C2×C8×C83—41no—
92C2×C8×C83—41no—
93C2×C8×C83—41no—
94C4⋊C4×C83—21no—
95C4⋊C4×C83—21no—
96C4⋊C4×C83—41no—
97C4⋊C4×C83—41no—
98C4⋊C4×C83—41no—
99C4⋊C4×C83—41no—
100C42×C83—41no—
101C42×C83—41no—
102C42×C83C2×D411yescharacteristic
103C42×C83C2×D411yescharacteristic
104C42×C83#4111yescharacteristic
105C42×C83#4111yescharacteristic
106C23×C83#12111yescharacteristic
107Q8×C83—22no—
108Q8×C83—22no—
109Q8×C83—41no—
110Q8×C83—41no—
111C2×C4×C83—22no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—41no—
116C2×C4×C83—41no—
117C2×C4×C83—81no—
118C2×C4×C83—81no—
119C2×C4×C83—81no—
120C2×C4×C83—81no—
121C2×C4×C83#12011yescharacteristic
122C2×C4×C83#12111yescharacteristic
123C2×C4×C83#12111yescharacteristic
124C2×C4×C83#12311yescharacteristic
125C2×C4×C83#12311yescharacteristic
126C2×C4×C83#12411yescharacteristic
127C2×C4×C83C2×Q1611yescharacteristic
128C2×C4×C83#13511yescharacteristic
129C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C83#13711yescharacteristic
131C2×Dic83—41no—
132C2×Dic83—41no—
133Dic166—81no—
134Dic166—81no—
135C8×C83—81no—
136C83⋊C8—42no—
137C83⋊C8—42no—
138C83⋊C8—81no—
139C22×C83—21no—
140C22×C83—21no—
141C22×C83#39411yescharacteristic
142C22×C83#46711yescharacteristic
143C22×C83#46811yescharacteristic
144C4×C83—21no—
145C4×C83—21no—
146C4×C83—21no—
147C4×C83—21no—
148C4×C83—42no—
149C4×C83—81no—
150C4×C83—161no—
151C4×C83#44911yescharacteristic
152C4×C83#45111yescharacteristic
153C4×C83#48411yescharacteristic
154C4×C83#48511yescharacteristic
155Dic83—81no—
156Dic83—81no—
157#10471—831nomaximal, Sylow
158C2×C83—21no—
159C2×C83—21no—
160C2×C83#203611yescharacteristic
161C2×C83#204911yescharacteristic
162C2×C83#205311yescharacteristic
163#3078—831no—
164#1805D8311yescharacteristic
165#1571—831no—
166#1542—831no—
167#1518—831no—
168#1461—831no—
169#1286—831no—
170C83#1047111yescharacteristic, complemented, Sylow
171#533—831no—
172C2×C4×Q8C2×D8311yescharacteristic
173#479—1662no—
174#477—1661no—
175#475—1661no—
176#431—831no—
177#431—831no—
178#428—1661no—
179#423—831no—
180C2×C4⋊C8C2×D8311yescharacteristic
181#419—1661no—
182C2×#103—21no—
183#382C2×D8311yescharacteristic
184#340—21no—
185#335—1662no—
186#333—1661no—
187#332—1661no—
188#328—1662no—
189#324—1662no—
190C22×Q8C22⋊D8311yescharacteristic
191C2×M16—1661no—
192C22×C8—21no—
193C4⋊Q8—831no—
194C4⋊Q8—831no—
195#125—1661no—
196C22⋊Q8—1661no—
197C22⋊Q8—1661no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—1661no—
203C4×Q8—1661no—
204#117—1661no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C22⋊D8311yescharacteristic
208C2×C42—21no—
209C2×C42C22×D8311yescharacteristic
210#107—1662no—
211#106—1662no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—832no—
215C4⋊C8—1661no—
216C4⋊C8—1661no—
217C4⋊C8—1661no—
218#103—42no—
219#103—1662no—
220#103—1662no—
221C22⋊C8—832no—
222C22⋊C8—1661no—
223C4×C8—1661no—
224C4×C8—1661no—
225#95—21no—
226#95—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—1661no—
233C2×Q8—1661no—
234C2×Q8#1305058012yes—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4D4×D8311yescharacteristic
239C22×C4C2×C22⋊D8311yescharacteristic
240C22×C4#1305058911yescharacteristic
241M16—3321no—
242M16—3321no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—3321no—
247C2×C8—1662no—
248C2×C8—1662no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—3321no—
256C4⋊C4—3321no—
257C4⋊C4—1661no—
258C4⋊C4—1661no—
259C4⋊C4—1661no—
260C4⋊C4—1661no—
261C22⋊C4—3321no—
262C42—41no—
263C42—41no—
264C42—3321no—
265C42D4×D8311yescharacteristic
266C42D4×D8311yescharacteristic
267C42#1305059011yescharacteristic
268C42#1305059011yescharacteristic
269C23#1458176411yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274Q8—6641no—
275Q8—6641no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—3321no—
287C2×C4—3321no—
288C2×C4#1458176011yescharacteristic
289C2×C4#1458176511yescharacteristic
290C2×C4#1458176511yescharacteristic
291C2×C4#1458177411yescharacteristic
292C2×C4#1458177511yescharacteristic
293C2×C4#1458177811yescharacteristic
294C2×C4C2×#1305058011yescharacteristic
295C2×C4#1458181211yescharacteristic
296C2×C4#1458181811yescharacteristic
297C2×C4#1458182211yescharacteristic
298C8—81no—
299C8—3322no—
300C8—3322no—
301C8—6641no—
302C22—21no—
303C22—21no—
304C22#1912761611yescharacteristic
305C22#1912794011yescharacteristic
306C22#1912794511yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—161no—
314C4—6641no—
315C4—6641no—
316C4#1912784411yescharacteristic
317C4#1912785611yescharacteristic
318C4#1912803611yescharacteristic
319C4#1912804211yescharacteristic
320C2—21no—
321C2—21no—
322C2#2490866611yescharacteristic
323C2#2490874111yescharacteristic
324C2#2490876711yescharacteristic
subgroupG/H
centerC22#19127616
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1805C2
socleC22×C83#394
prime radicalC23×C83#121
hypercenter#1805D83
hypocenterC83#10471
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
170. C83#10471semidirect

Maximal subgroups

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

subgroupindex
#249172682
#249062372
#249061212
#249060262
#249057872
#249053212
C83×#18052
#1047183