Finite Group Databasebeta

← #14739085

Subgroups — #14739085

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079574C211yesmaximal, characteristic
2#13078746C211yesmaximal, characteristic, complemented
3#13078647C211yesmaximal, characteristic
4#13068060C212yesmaximal, complemented
5#13068046C212yesmaximal, complemented
6#13067986C212yesmaximal, complemented
7#13067964C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067319C211yesmaximal, characteristic
10#13067280C211yesmaximal, characteristic, complemented
11C11×#2982C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13#10623008C2211yescharacteristic
14#10623001C2211yescharacteristic
15C8×Q8×C11—22no—
16C8×Q8×C11C2212yes—
17C8×Q8×C11C2212yes—
18C11×#431—22no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622841—21no—
22#10622840—21no—
23#10622644C2212yes—
24#10622643—22no—
25#10622640C2212yes—
26C4×#4325—22no—
27#10622633C2212yes—
28#10622633C2212yes—
29#10622584—21no—
30#10622581—21no—
31#10622539C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622458—22no—
34#10622346—22no—
35#10622312C2211yescharacteristic
36#10622307C2211yescharacteristic
37#10622306C2211yescharacteristic
38#10622294C2211yescharacteristic
39#10622124C2212yes—
40#10622123C2212yes—
41#10622120C2212yes—
42#10622120C2212yes—
43#10622096C2212yes—
44#10622095C2212yes—
45C22×Q8×C11D411yescharacteristic
46C2×#4339—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11D412yes—
50C4×Q8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4326—22no—
56C2×#4325—22no—
57#66983—21no—
58#66983—21no—
59#66979—21no—
60#66977—21no—
61#66977—21no—
62C2×Dic44—22no—
63C2×#4314—22no—
64#66928—21no—
65#66927C2311yescharacteristic
66C4×D44—21no—
67C4×D44—21no—
68#66923—21no—
69#66922C2311yescharacteristic
70#66922C2311yescharacteristic
71#66922C2311yescharacteristic
72C4×Dic22—21no—
73C4×Dic22—21no—
74C11×C4⋊C8—22no—
75C11×C4⋊C8—22no—
76C11×C4⋊C8D412yes—
77C11×C4⋊C8C2312yes—
78C11×C22⋊C8—21no—
79C11×C22⋊C8D412yes—
80C4×C8×C11—22no—
81C4×C8×C11—22no—
82C4×C8×C11—21no—
83C4×C8×C11C2311yescharacteristic
84C4×C8×C11C2311yescharacteristic
85#66899—22no—
86#66899—22no—
87C22⋊(C11⋊C8)—21no—
88C22⋊(C11⋊C8)—21no—
89#66885—22no—
90#66880—22no—
91#66874—22no—
92#66873—22no—
93#66872—22no—
94#66872—22no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2312yes—
97#66867—21no—
98C4×C11⋊C8—21no—
99#19400—111nomaximal, Sylow
100C2×Q8×C11—24no—
101C2×Q8×C11—21no—
102C2×Q8×C11C2×D412yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—41no—
109#4339—82no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×C4×D11—41no—
114C2×Dic22—21no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×C8×C11—22no—
118C2×C8×C11C2×D412yes—
119C2×C8×C11C2×D412yes—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4C2×D412yes—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C42×C11C2411yescharacteristic
130C22⋊Dic11—41no—
131#4326—44no—
132#4325—44no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141Dic11⋊C4—41no—
142Dic11⋊C4—41no—
143C4×Dic11—41no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146Dic44—82no—
147#4314—82no—
148#3210—111no—
149#3113—111no—
150#3103—111no—
151#2982D1111yescharacteristic, complemented
152#1682—112no—
153#1680—112no—
154#1670—112no—
155#1666—112no—
156#1572—111no—
157#1553—111no—
158#1544—111no—
159C23×C11#12111yescharacteristic
160C22×D11—41no—
161Q8×C11—24no—
162Q8×C11—22no—
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—81no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C22⋊D11—82no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181D44—42no—
182D44—42no—
183D44—81no—
184C4×D11—82no—
185Dic22—42no—
186Dic22—42no—
187Dic22—42no—
188C8×C11—22no—
189C8×C11—22no—
190C8×C11—42no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193#533—111no—
194#532—111no—
195C2×C4×Q8C2×D1111yescharacteristic
196#494—111no—
197#492—111no—
198#487—111no—
199#486—111no—
200#483—221no—
201#481—221no—
202#475—112no—
203#475—112no—
204#464—222no—
205#462—112no—
206#460—112no—
207#452—222no—
208#451—221no—
209#448—221no—
210C8×Q8—22no—
211C8×Q8C2×D1112yes—
212C8×Q8C2×D1112yes—
213#441—222no—
214C4×SD16—222no—
215#432—111no—
216#431—22no—
217#431—111no—
218#431C2×D1111yescharacteristic
219#431C2×D1111yescharacteristic
220#335—112no—
221#334—112no—
222#332—112no—
223#332—112no—
224#332—112no—
225#331—112no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11C2×#12111yescharacteristic
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C4×C11—21no—
234C4×C11—24no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—42no—
239C4×C11C2×#13512yes—
240C4×C11#57712yes—
241Dic11—81no—
242Dic11—81no—
243Dic11—81no—
244C2×#41—221no—
245C22×Q8D4411yescharacteristic
246C2×Q16—222no—
247C2×Q16—222no—
248C2×SD16—222no—
249C2×SD16—222no—
250C4⋊Q8—111no—
251C4⋊Q8—111no—
252C4⋊Q8—111no—
253#127—111no—
254#125—221no—
255#124—221no—
256C22⋊Q8—221no—
257C22⋊Q8—221no—
258#121—221no—
259#121—221no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—221no—
263C4×Q8—221no—
264C4×Q8D4412yes—
265C4×Q8C22×D1112yes—
266C4×D4—221no—
267C4×D4—221no—
268#117—221no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4D4411yescharacteristic
271C2×C42—21no—
272C2×C42C22×D1111yescharacteristic
273#106—222no—
274#106—222no—
275C4⋊C8—22no—
276C4⋊C8—22no—
277C4⋊C8—112no—
278C4⋊C8—112no—
279C4⋊C8C22⋊D1112yes—
280C4⋊C8C22×D1112yes—
281#103—222no—
282#103—222no—
283#103—222no—
284#103—222no—
285#102—222no—
286#102—222no—
287C22⋊C8—21no—
288C22⋊C8—221no—
289C22⋊C8—221no—
290C22⋊C8C22⋊D1112yes—
291#97—221no—
292C4×C8—22no—
293C4×C8—22no—
294C4×C8—21no—
295C4×C8—221no—
296C4×C8C22×D1111yescharacteristic
297C4×C8C22×D1111yescharacteristic
298C2×C11—41no—
299C2×C11#304311yescharacteristic
300C2×C11#305011yescharacteristic
301C2×C11#306911yescharacteristic
302D11—161no—
303#41—882no—
304C2×Q8—24no—
305C2×Q8—21no—
306C2×Q8—221no—
307C2×Q8—221no—
308C2×Q8—221no—
309C2×Q8C2×D4412yes—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—441no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—441no—
317C22×C4C2×D4411yescharacteristic
318C22×C4#433911yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320Q16—444no—
321Q16—882no—
322SD16—444no—
323SD16—882no—
324C2×C8—22no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8C2×C22⋊D1112yes—
328C2×C8C2×C22⋊D1112yes—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4C2×D4412yes—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C42—22no—
345C42—22no—
346C42—441no—
347C42C2×D4411yescharacteristic
348C42#433911yescharacteristic
349C42C2×C22⋊D1111yescharacteristic
350C42C23×D1111yescharacteristic
351C11#1940011yescharacteristic, complemented, Sylow
352C23—441no—
353C23#6698311yescharacteristic
354Q8—24no—
355Q8—22no—
356Q8—442no—
357Q8—442no—
358Q8—442no—
359Q8#6695714yes—
360D4—442no—
361D4—442no—
362D4—881no—
363D4—882no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—882no—
375C2×C4#6698311yescharacteristic
376C2×C4#6698311yescharacteristic
377C2×C4#6698311yescharacteristic
378C2×C4C22×D4411yescharacteristic
379C2×C4C2×#433911yescharacteristic
380C2×C4C22×C22⋊D1111yescharacteristic
381C8—22no—
382C8—22no—
383C8—42no—
384C8—442no—
385C8—442no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22C2×#6698311yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—24no—
397C4—21no—
398C4—42no—
399C4—881no—
400C4—881no—
401C4—881no—
402C4C2×#6695712yes—
403C4#1062336812yes—
404C2—41no—
405C2—1761no—
406C2#1307813711yescharacteristic
407C2#1307819711yescharacteristic
408C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2982C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2982D11
hypocenterC11#19400
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #13078746C2semidirect
4. #13068060C2semidirect
5. #13068046C2semidirect
6. #13067986C2semidirect
7. #13067964C2semidirect
8. #13067396C2semidirect
10. #13067280C2semidirect
11. C11×#2982C2semidirect
151. #2982D11semidirect
351. C11#19400semidirect

Maximal subgroups

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

subgroupindex
#130795742
#130787462
#130786472
#130680602
#130680462
#130679862
#130679642
#130673962
#130673192
#130672802
C11×#29822
#1940011