Finite Group Databasebeta

← #14739140

Subgroups — #14739140

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079752C211yesmaximal, characteristic
2#13078738C211yesmaximal, characteristic
3#13077697C211yesmaximal, characteristic, complemented
4#13068062C212yesmaximal, complemented
5#13068034C212yesmaximal, complemented
6#13068018C212yesmaximal, complemented
7#13067996C212yesmaximal, complemented
8#13067394C211yesmaximal, characteristic, complemented
9#13067326C211yesmaximal, characteristic, complemented
10#13067276C211yesmaximal, characteristic
11C11×#3104C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#484—21no—
16C11×#477C2212yes—
17C11×#462C2212yes—
18C11×#451—21no—
19C4×C11×Q16—22no—
20C11×#431C2211yescharacteristic
21#10622840—21no—
22#10622701C2211yescharacteristic
23#10622701C2211yescharacteristic
24#10622692C2211yescharacteristic
25#10622691C2211yescharacteristic
26#10622679—22no—
27#10622640C2212yes—
28#10622639—22no—
29Q8×C11⋊C8—22no—
30Q8×C11⋊C8C2212yes—
31Q8×C11⋊C8C2212yes—
32#10622634C2212yes—
33#10622616—22no—
34#10622580—21no—
35#10622539C2211yescharacteristic
36#10622538—22no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622185C2212yes—
40#10622184C2212yes—
41#10622123C2212yes—
42#10622119C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45C22×Q8×C11D411yescharacteristic
46C2×#4339—21no—
47C2×C11×Q16—22no—
48C11×C4⋊Q8C2311yescharacteristic
49C11×C4⋊Q8C2311yescharacteristic
50C11×#125—21no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11D412yes—
58C4×Q8×C11C2312yes—
59C11×#117—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4325—22no—
65#66983—21no—
66#66983—21no—
67#66928—21no—
68#66927C2311yescharacteristic
69C4×D44—21no—
70C4×D44—21no—
71#66922C2311yescharacteristic
72C11×#107—22no—
73C11×C4⋊C8C2312yes—
74C11×#103—22no—
75C11×#103—22no—
76C11×C22⋊C8—21no—
77C4×C8×C11—21no—
78#66899—22no—
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—21no—
81C22⋊(C11⋊C8)D412yes—
82#66873—22no—
83#66873—22no—
84#66873—22no—
85#66872—22no—
86#66871—22no—
87#66871—22no—
88C4⋊(C11⋊C8)—22no—
89C4⋊(C11⋊C8)—22no—
90C4⋊(C11⋊C8)D412yes—
91C4⋊(C11⋊C8)C2312yes—
92C4⋊(C11⋊C8)C2312yes—
93#66867—21no—
94C4×C11⋊C8—21no—
95C4×C11⋊C8—22no—
96C4×C11⋊C8—22no—
97C4×C11⋊C8C2311yescharacteristic
98C4×C11⋊C8C2311yescharacteristic
99#19406—111nomaximal, Sylow
100C2×Q8×C11—24no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11C2×D412yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×C22⋊D11—41no—
111#4339—82no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C11×Q16—44no—
118C2×C8×C11—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4C2×D412yes—
129C11×C22⋊C4—41no—
130C42×C11—22no—
131C42×C11—22no—
132C42×C11—41no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11#4111yescharacteristic
136C42×C11C2411yescharacteristic
137#4325—44no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8C2×D412yes—
145C2×C11⋊C8C2×D412yes—
146#3228—111no—
147#3112—111no—
148#3104D1111yescharacteristic, complemented
149#2982—111no—
150#1682—112no—
151#1678—112no—
152#1676—112no—
153#1672—112no—
154#1572—111no—
155#1554—111no—
156#1543—111no—
157C23×C11#12111yescharacteristic
158C22×D11—41no—
159Q8×C11—24no—
160Q8×C11—22no—
161Q8×C11—42no—
162Q8×C11—81no—
163Q8×C11#13514yes—
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—81no—
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C22⋊D11—82no—
180C2×Dic11—41no—
181D44—42no—
182D44—42no—
183D44—81no—
184C4×D11—82no—
185Dic22—81no—
186C8×C11—42no—
187C11⋊C8—22no—
188C11⋊C8—22no—
189C11⋊C8—42no—
190C11⋊C8—42no—
191#533C2×D1111yescharacteristic
192#532—111no—
193C2×C4×Q8C2×D1111yescharacteristic
194#500—111no—
195#498—111no—
196#486—111no—
197#486—111no—
198#484—21no—
199#482—222no—
200#480—221no—
201#478—222no—
202#477—112no—
203#477C2×D1112yes—
204#462C2×D1112yes—
205#460—112no—
206#451—21no—
207#448—221no—
208C8×Q8—112no—
209C8×Q8—112no—
210C8×Q8—222no—
211#440—222no—
212C4×Q16—22no—
213#432—111no—
214#431—111no—
215#431—111no—
216#431—222no—
217#431C2×D1111yescharacteristic
218#335—112no—
219#334—112no—
220#333—112no—
221#333—112no—
222#332—112no—
223#331—112no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11C2×#12111yescharacteristic
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C4×C11—21no—
232C4×C11—24no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—42no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11C2×#13512yes—
240C4×C11#57812yes—
241Dic11—81no—
242C2×#41—221no—
243C22×Q8C22⋊D1111yescharacteristic
244C2×Q16—22no—
245C2×SD16—222no—
246C4⋊Q8—111no—
247C4⋊Q8C22×D1111yescharacteristic
248C4⋊Q8C22×D1111yescharacteristic
249#127—111no—
250#125—21no—
251#124—221no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254#121—221no—
255#121—221no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8C22⋊D1112yes—
261C4×Q8C22×D1112yes—
262C4×D4—221no—
263C4×D4—221no—
264#117—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C22⋊D1111yescharacteristic
267C2×C42—21no—
268C2×C42C22×D1111yescharacteristic
269#107—22no—
270#107—222no—
271#107—222no—
272#106—222no—
273C4⋊C8—112no—
274C4⋊C8—112no—
275C4⋊C8—112no—
276C4⋊C8—222no—
277C4⋊C8—222no—
278C4⋊C8C22×D1112yes—
279#103—22no—
280#103—22no—
281#103—222no—
282#102—222no—
283#102—222no—
284#102—222no—
285C22⋊C8—21no—
286C22⋊C8—112no—
287C22⋊C8—221no—
288C22⋊C8—221no—
289#97—221no—
290C4×C8—21no—
291C4×C8—111no—
292C4×C8—111no—
293C4×C8—222no—
294C4×C8—222no—
295C4×C8—221no—
296C2×C11—41no—
297C2×C11#304411yescharacteristic
298C2×C11#305011yescharacteristic
299C2×C11#306811yescharacteristic
300D11—161no—
301#41—882no—
302C2×Q8—24no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—221no—
307C2×Q8C2×C22⋊D1112yes—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—441no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—441no—
315C22×C4D4×D1111yescharacteristic
316C22×C4#434111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318Q16—44no—
319SD16—444no—
320C2×C8—22no—
321C2×C8—112no—
322C2×C8—112no—
323C2×C8—222no—
324C2×C8—222no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4C2×C22⋊D1112yes—
337C22⋊C4—41no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C42—22no—
341C42—22no—
342C42—41no—
343C42D4×D1111yescharacteristic
344C42#434111yescharacteristic
345C42C2×C22⋊D1111yescharacteristic
346C42C23×D1111yescharacteristic
347C11#1940611yescharacteristic, complemented, Sylow
348C23—441no—
349C23#6699211yescharacteristic
350Q8—24no—
351Q8—22no—
352Q8—42no—
353Q8—81no—
354Q8—881no—
355Q8#6700314yes—
356D4—442no—
357D4—442no—
358D4—881no—
359D4—882no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—441no—
370C2×C4—882no—
371C2×C4#6699211yescharacteristic
372C2×C4#6699211yescharacteristic
373C2×C4#6699211yescharacteristic
374C2×C4C2×D4×D1111yescharacteristic
375C2×C4C2×#434111yescharacteristic
376C2×C4C22×C22⋊D1111yescharacteristic
377C8—42no—
378C8—222no—
379C8—222no—
380C8—442no—
381C8—442no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22C2×#6699211yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—24no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4—881no—
398C4#1062329712yes—
399C4C2×#6700312yes—
400C2—41no—
401C2—1761no—
402C2#1307814311yescharacteristic
403C2#1307819411yescharacteristic
404C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3104C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3104D11
hypocenterC11#19406
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #13077697C2semidirect
4. #13068062C2semidirect
5. #13068034C2semidirect
6. #13068018C2semidirect
7. #13067996C2semidirect
8. #13067394C2semidirect
9. #13067326C2semidirect
11. C11×#3104C2semidirect
148. #3104D11semidirect
347. C11#19406semidirect

Maximal subgroups

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

subgroupindex
#130797522
#130787382
#130776972
#130680622
#130680342
#130680182
#130679962
#130673942
#130673262
#130672762
C11×#31042
#1940611