Finite Group Databasebeta

← #14736913

Subgroups — #14736913

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079741C211yesmaximal, characteristic, complemented
2#13079531C211yesmaximal, characteristic
3C2×#10622307C211yesmaximal, characteristic, complemented
4#13068149C214yesmaximal, complemented
5#13068025C214yesmaximal, complemented
6#13067364C211yesmaximal, characteristic, complemented
7#13067298C211yesmaximal, characteristic, complemented
8#13067285C211yesmaximal, characteristic, complemented
9C11×#2931C211yesmaximal, characteristic, complemented
10C2×C11×#131—21no—
11C11×#532C2211yescharacteristic
12C2×#66927C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#436—21no—
15C11×#436C2212yescomplemented
16C8×D4×C11—21no—
17C8×D4×C11C2212yescomplemented
18C11×#423C2211yescharacteristic
19C11×#408—21no—
20C2×C4×C8×C11C2211yescharacteristic
21C2×#66885—21no—
22C2×#66885—21no—
23#10622701—21no—
24#10622692—21no—
25#10622686—21no—
26#10622683—21no—
27#10622649—22no—
28#10622647—22no—
29#10622628C2214yes—
30#10622621C2214yescomplemented
31#10622538C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622307—21no—
34#10622307—21no—
35#10622307C2212yes—
36#10622307C2212yes—
37#10622123C2214yes—
38#10622119C2214yescomplemented
39#10622096C2212yescomplemented
40#10622095C2212yescomplemented
41C2×C11×#41—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×Dic22—21no—
46C11×#131—44no—
47C2×C11×M16—21no—
48C2×C11×M16—22no—
49C22×C8×C11—22no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×C4⋊Q8D411yescharacteristic
53C11×#127D411yescharacteristic
54C11×#124—21no—
55C11×#121—21no—
56C11×#121D412yes—
57C4×D4×C11—21no—
58C4×D4×C11C2312yes—
59C2×C42×C11C2311yescharacteristic
60C2×#4323—24no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63#66927—21no—
64#66927—21no—
65#66927—21no—
66#66927C2312yes—
67#66922—21no—
68#66922—21no—
69#66922—21no—
70#66922C2312yes—
71C11×C4⋊C8—21no—
72C11×C4⋊C8C2312yes—
73C11×C22⋊C8—22no—
74C11×C22⋊C8—22no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66896—24no—
80C22⋊(C11⋊C8)—21no—
81C22⋊(C11⋊C8)—21no—
82#66885—22no—
83#66885—22no—
84#66885—22no—
85#66885—22no—
86#66873—24no—
87#66872—24no—
88C4⋊(C11⋊C8)C2312yes—
89C4⋊(C11⋊C8)C2312yes—
90C4×C11⋊C8—21no—
91C4×C11⋊C8—21no—
92#19196—111nomaximal, Sylow
93C23×D11—41no—
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11C2×D412yes—
101C22×C4×C11—22no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×Dic11—41no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×D44—42no—
113C2×D44—42no—
114C2×D44—82no—
115C2×D44—82no—
116C2×Dic22—22no—
117C2×Dic22—41no—
118C2×Dic22—82no—
119C11×M16—44no—
120C11×M16—42no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—44no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C11×C4⋊C4—21no—
130C11×C4⋊C4C2×D412yes—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—22no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11#4111yescharacteristic
136C42×C11C2411yescharacteristic
137#4323—84no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—41no—
141C4⋊Dic11—41no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144#3227—111no—
145#3205—111no—
146C2×#486—111no—
147#2931D1111yescharacteristic, complemented
148#1697—114no—
149#1677—114no—
150#1564—111no—
151#1548—111no—
152#1545—111no—
153C23×C11—22no—
154C23×C11#12111yescharacteristic
155C22×D11—42no—
156C22×D11—82no—
157C22×D11—82no—
158C22×D11—82no—
159Q8×C11—42no—
160D4×C11—24no—
161D4×C11—44no—
162D4×C11—42no—
163D4×C11—42no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#13512yes—
173C2×C4×C11AGL(1,ℤ/8)12yes—
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×Dic11—42no—
178C2×Dic11—82no—
179D44—42no—
180D44—42no—
181D44—44no—
182D44—82no—
183D44—82no—
184D44—82no—
185D44—82no—
186Dic22—82no—
187Dic22—82no—
188C8×C11—21no—
189C8×C11—21no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—42no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195C2×#131—21no—
196#532C2×D1111yescharacteristic
197C2×C4⋊Q8—111no—
198C2×#127—111no—
199#498—221no—
200#493—221no—
201#486—112no—
202#486—112no—
203#486—221no—
204#486—221no—
205#486—221no—
206#486—221no—
207#481—222no—
208#476—114no—
209#459—114no—
210#447—222no—
211#436—21no—
212#436C2×D1112yescomplemented
213C8×D4—21no—
214C8×D4C2×D1112yescomplemented
215#431—111no—
216#431—111no—
217#423C2×D1111yescharacteristic
218C2×#102—221no—
219C2×#102—221no—
220#408—21no—
221C2×C4×C8C2×D1111yescharacteristic
222#335—112no—
223#334—112no—
224#333—114no—
225#331—114no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11#46312yes—
232C22×C11C2×#12111yescharacteristic
233C2×D11—82no—
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—164no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—42no—
240C4×C11#46312yes—
241C4×C11#47212yes—
242C4×C11C2×#13511yescharacteristic
243C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C11#57712yes—
245Dic11—82no—
246C2×#41—21no—
247C22×Q8—221no—
248C22×D4—221no—
249C22×D4—221no—
250C22×D4—221no—
251C2×D8—224no—
252#131—44no—
253C2×M16—21no—
254C2×M16—22no—
255C22×C8—22no—
256C22×C8C22⋊D1111yescharacteristic
257C22×C8C22⋊D1111yescharacteristic
258C4⋊Q8—112no—
259C4⋊Q8—221no—
260C4⋊Q8—221no—
261C4⋊Q8—221no—
262C4⋊Q8D4411yescharacteristic
263#127—112no—
264#127—221no—
265#127—221no—
266#127—221no—
267#127D4411yescharacteristic
268#124—21no—
269#121—21no—
270#121D4412yes—
271C4×D4—21no—
272C4×D4C22×D1112yes—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C42C22×D1111yescharacteristic
276#106—224no—
277C4⋊C8—21no—
278C4⋊C8—112no—
279C4⋊C8—112no—
280C4⋊C8C22×D1112yes—
281#102—224no—
282#102—222no—
283#102—222no—
284#102—222no—
285#102—222no—
286#102—224no—
287C22⋊C8—22no—
288C22⋊C8—22no—
289C22⋊C8—221no—
290C22⋊C8—221no—
291C4×C8—221no—
292C4×C8—221no—
293C4×C8C22⋊D1111yescharacteristic
294C4×C8C22⋊D1111yescharacteristic
295C4×C8C22×D1111yescharacteristic
296C4×C8C22×D1111yescharacteristic
297C2×C11—22no—
298C2×C11—82no—
299C2×C11C2×#46311yescharacteristic
300C2×C11#305711yescharacteristic
301C2×C11C2×#47211yescharacteristic
302D11—162no—
303C24—441no—
304#41—42no—
305#41—42no—
306C2×Q8—21no—
307C2×Q8—222no—
308C2×Q8—441no—
309C2×Q8—882no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—222no—
314C2×D4—222no—
315C2×D4—222no—
316C2×D4—441no—
317C2×D4—441no—
318C2×D4—441no—
319C2×D4—442no—
320C2×D4—442no—
321C2×D4—882no—
322C2×D4—882no—
323C2×D4C2×D4412yes—
324C22×C4—22no—
325C22×C4—441no—
326C22×C4C2×D4411yescharacteristic
327C22×C4#433911yescharacteristic
328C22×C4C2×C22⋊D1111yescharacteristic
329D8—884no—
330M16—44no—
331M16—42no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—44no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8C2×C22⋊D1111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C2×C22⋊D1111yescharacteristic
342C4⋊C4—21no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C4⋊C4C2×D4412yes—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C42C2×D4411yescharacteristic
351C42#433911yescharacteristic
352C42C2×C22⋊D1111yescharacteristic
353C42C23×D1111yescharacteristic
354C11#1919611yescharacteristic, complemented, Sylow
355C23—22no—
356C23—442no—
357C23—882no—
358C23—882no—
359C23—882no—
360C23#6698311yescharacteristic
361Q8—42no—
362Q8—882no—
363Q8—882no—
364D4—24no—
365D4—44no—
366D4—42no—
367D4—42no—
368D4—444no—
369D4—442no—
370D4—442no—
371D4—882no—
372D4—882no—
373D4—882no—
374D4—882no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—442no—
381C2×C4—882no—
382C2×C4#6698311yescharacteristic
383C2×C4#6698311yescharacteristic
384C2×C4#6698311yescharacteristic
385C2×C4#6698512yes—
386C2×C4#6700312yes—
387C2×C4C22×D4411yescharacteristic
388C2×C4C2×#433911yescharacteristic
389C2×C4C22×C22⋊D1111yescharacteristic
390C8—21no—
391C8—21no—
392C8—21no—
393C8—21no—
394C8—42no—
395C8—442no—
396C8—442no—
397C22—21no—
398C22—21no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—882no—
403C22—882no—
404C22—882no—
405C22—1764no—
406C22#1062262912yes—
407C22C2×#6698311yescharacteristic
408C4—21no—
409C4—21no—
410C4—42no—
411C4—882no—
412C4#1062262912yes—
413C4#1062275512yes—
414C4#1062328212yes—
415C4C2×#6698511yescharacteristic
416C4C2×#6700311yescharacteristic
417C2—22no—
418C2—82no—
419C2—1762no—
420C2C2×#1062262911yescharacteristic
421C2#1307825511yescharacteristic
422C2C2×#1062275511yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2931C2
socleC22×C11C2×#121
prime radical#13079531C2
hypercenter#2931D11
hypocenterC11#19196
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2931

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
3. C2×#10622307C2semidirect
4. #13068149C2semidirect
5. #13068025C2semidirect
6. #13067364C2semidirect
7. #13067298C2semidirect
8. #13067285C2semidirect
9. C11×#2931C2semidirect
15. C11×#436C22semidirect
17. C8×D4×C11C22semidirect
30. #10622621C22semidirect
38. #10622119C22semidirect
39. #10622096C22semidirect
40. #10622095C22semidirect
147. #2931D11semidirect
212. #436C2×D11semidirect
214. C8×D4C2×D11semidirect
354. C11#19196semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130795312
C2×#106223072
#130681492
#130680252
#130673642
#130672982
#130672852
C11×#29312
#1919611