Finite Group Databasebeta

← #14736909

Subgroups — #14736909

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#13079744C211yesmaximal, characteristic, complemented
2#13079534C211yesmaximal, characteristic
3#13077329C211yesmaximal, characteristic, complemented
4#13068146C214yesmaximal, complemented
5#13068022C214yesmaximal, complemented
6#13067364C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067284C211yesmaximal, characteristic, complemented
9C2×C11×#486C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×#66954—21no—
13#10623008C2211yescharacteristic
14C11×#486—21no—
15C11×#486—21no—
16C11×#486C2212yes—
17C11×#486C2212yes—
18C2×C11×#102—21no—
19C2×C11×#102—21no—
20C2×C4×C8×C11C2211yescharacteristic
21#10622830—22no—
22#10622723—21no—
23#10622701—21no—
24#10622697C2214yescomplemented
25#10622692—21no—
26#10622686—21no—
27#10622685C2214yes—
28#10622683—21no—
29#10622581—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622301—21no—
34#10622301C2212yescomplemented
35C8×D44—21no—
36C8×D44C2212yescomplemented
37#10622184C2214yescomplemented
38#10622182C2214yes—
39#10622096C2212yescomplemented
40#10622095C2212yescomplemented
41C22×Q8×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C2×#4339—21no—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11D411yescharacteristic
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8C2312yes—
52C11×#127—21no—
53C11×#127—21no—
54C11×#127—21no—
55C11×#127C2312yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4323—24no—
60#66983—21no—
61#66983D412yes—
62C2×#4318—21no—
63#66954—44no—
64C2×#4313—22no—
65C2×C8×D11—22no—
66#66928—21no—
67#66927D411yescharacteristic
68C4×D44—21no—
69C4×D44C2312yes—
70#66922D411yescharacteristic
71C11×#102—22no—
72C11×#102—22no—
73C11×#102—22no—
74C11×#102—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(C2×D11)⋊C8—22no—
83(C2×D11)⋊C8—22no—
84#66873—24no—
85#66872—24no—
86C4⋊(C11⋊C8)—21no—
87C4⋊(C11⋊C8)C2312yes—
88C4⋊(C11⋊C8)C2312yes—
89C4⋊(C11⋊C8)C2312yes—
90C4×C11⋊C8—21no—
91C4×C11⋊C8—21no—
92#19196—111nomaximal, Sylow
93C24×C11—41no—
94C2×Q8×C11—22no—
95C2×Q8×C11—41no—
96C2×Q8×C11—82no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—82no—
106C2×D4×C11—82no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C2×C22⋊D11—22no—
112#4339—42no—
113#4339—42no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44C2×D412yes—
117C2×C4×D11—22no—
118C2×Dic22—21no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11C2411yescharacteristic
133#4323—84no—
134(C2×D11)⋊C4—22no—
135(C2×D11)⋊C4—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11C2×D412yes—
138#4318—42no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142#4313—44no—
143C8×D11—44no—
144#3227—111no—
145#3205—111no—
146C2×#486D1111yescharacteristic, complemented
147#2931—111no—
148#1697—114no—
149#1677—114no—
150#1564—111no—
151#1548—111no—
152#1545—111no—
153C23×C11—42no—
154C23×C11—82no—
155C23×C11—82no—
156C23×C11—82no—
157C23×C11#12111yescharacteristic
158C22×D11—22no—
159Q8×C11—82no—
160Q8×C11—82no—
161D4×C11—42no—
162D4×C11—42no—
163D4×C11—44no—
164D4×C11—82no—
165D4×C11—82no—
166D4×C11—82no—
167D4×C11—82no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—42no—
171C2×C4×C11—82no—
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#13512yes—
176C2×C4×C11AGL(1,ℤ/8)12yes—
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C22⋊D11—44no—
181C2×Dic11—22no—
182D44—24no—
183D44—42no—
184D44—42no—
185C4×D11—42no—
186C4×D11—42no—
187Dic22—42no—
188C8×C11—21no—
189C8×C11—21no—
190C8×C11—21no—
191C8×C11—21no—
192C11⋊C8—42no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195C2×#131—221no—
196#532—111no—
197C2×C4⋊Q8C2×D1111yescharacteristic
198C2×#127C2×D1111yescharacteristic
199#498—221no—
200#493—221no—
201#486—21no—
202#486—21no—
203#486—221no—
204#486—221no—
205#486C2×D1112yes—
206#486C2×D1112yes—
207#481—222no—
208#476—114no—
209#459—114no—
210#447—222no—
211#436—112no—
212#436—221no—
213C8×D4—112no—
214C8×D4—221no—
215#431—111no—
216#431—111no—
217#423—111no—
218C2×#102—21no—
219C2×#102—21no—
220#408—221no—
221C2×C4×C8C2×D1111yescharacteristic
222#335—112no—
223#334—112no—
224#333—114no—
225#331—114no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—82no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—164no—
232C22×C11#46312yes—
233C22×C11C2×#12111yescharacteristic
234C2×D11—42no—
235C2×D11—42no—
236C2×D11—42no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—82no—
240C4×C11#46312yes—
241C4×C11#47212yes—
242C4×C11C2×#13511yescharacteristic
243C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C11#57712yes—
245Dic11—42no—
246C2×#41—221no—
247C22×Q8—21no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C2×D8—224no—
252#131—444no—
253C2×M16—221no—
254C2×M16—222no—
255C22×C8—222no—
256C22×C8C22⋊D1111yescharacteristic
257C22×C8C22⋊D1111yescharacteristic
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—111no—
262C4⋊Q8C22×D1112yes—
263#127—21no—
264#127—21no—
265#127—21no—
266#127—111no—
267#127C22×D1112yes—
268#124—221no—
269#121—112no—
270#121—221no—
271C4×D4—112no—
272C4×D4—221no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C42C22×D1111yescharacteristic
276#106—224no—
277C4⋊C8—112no—
278C4⋊C8—112no—
279C4⋊C8—112no—
280C4⋊C8—221no—
281#102—22no—
282#102—22no—
283#102—22no—
284#102—22no—
285#102—224no—
286#102—224no—
287C22⋊C8—221no—
288C22⋊C8—221no—
289C22⋊C8—222no—
290C22⋊C8—222no—
291C4×C8—221no—
292C4×C8—221no—
293C4×C8C22⋊D1111yescharacteristic
294C4×C8C22⋊D1111yescharacteristic
295C4×C8C22×D1111yescharacteristic
296C4×C8C22×D1111yescharacteristic
297C2×C11—22no—
298C2×C11—162no—
299C2×C11C2×#46311yescharacteristic
300C2×C11#305711yescharacteristic
301C2×C11C2×#47211yescharacteristic
302D11—82no—
303C24—41no—
304#41—442no—
305#41—442no—
306C2×Q8—22no—
307C2×Q8—41no—
308C2×Q8—82no—
309C2×Q8—221no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—82no—
319C2×D4—82no—
320C2×D4—112no—
321C2×D4—222no—
322C2×D4—221no—
323C2×D4—221no—
324C22×C4—41no—
325C22×C4—222no—
326C22×C4D4×D1111yescharacteristic
327C22×C4#434111yescharacteristic
328C22×C4C2×C22⋊D1111yescharacteristic
329D8—884no—
330M16—444no—
331M16—442no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—444no—
338C2×C8C2×C22⋊D1111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C2×C22⋊D1111yescharacteristic
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—112no—
347C4⋊C4—221no—
348C22⋊C4—222no—
349C22⋊C4—222no—
350C42D4×D1111yescharacteristic
351C42#434111yescharacteristic
352C42C2×C22⋊D1111yescharacteristic
353C42C23×D1111yescharacteristic
354C11#1919611yescharacteristic, complemented, Sylow
355C23—42no—
356C23—82no—
357C23—82no—
358C23—82no—
359C23—222no—
360C23#6699111yescharacteristic
361Q8—82no—
362Q8—82no—
363Q8—442no—
364D4—44no—
365D4—42no—
366D4—42no—
367D4—82no—
368D4—82no—
369D4—82no—
370D4—82no—
371D4—224no—
372D4—444no—
373D4—442no—
374D4—442no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—42no—
378C2×C4—82no—
379C2×C4—222no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4#6699111yescharacteristic
383C2×C4#6699111yescharacteristic
384C2×C4#6699111yescharacteristic
385C2×C4#6700212yes—
386C2×C4#6700312yes—
387C2×C4C2×D4×D1111yescharacteristic
388C2×C4C2×#434111yescharacteristic
389C2×C4C22×C22⋊D1111yescharacteristic
390C8—21no—
391C8—21no—
392C8—21no—
393C8—21no—
394C8—442no—
395C8—442no—
396C8—442no—
397C22—21no—
398C22—21no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—164no—
403C22—442no—
404C22—442no—
405C22—442no—
406C22#1062267012yes—
407C22C2×#6699111yescharacteristic
408C4—21no—
409C4—21no—
410C4—82no—
411C4—442no—
412C4#1062267012yes—
413C4#1062277312yes—
414C4#1062329312yes—
415C4C2×#6700211yescharacteristic
416C4C2×#6700311yescharacteristic
417C2—22no—
418C2—162no—
419C2—882no—
420C2C2×#1062267011yescharacteristic
421C2#1307825111yescharacteristic
422C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC22×C11C2×#121
prime radical#13079534C2
hypercenterC2×#486D11
hypocenterC11#19196
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13079744C2semidirect
3. #13077329C2semidirect
4. #13068146C2semidirect
5. #13068022C2semidirect
6. #13067364C2semidirect
7. #13067297C2semidirect
8. #13067284C2semidirect
9. C2×C11×#486C2semidirect
24. #10622697C22semidirect
34. #10622301C22semidirect
36. C8×D44C22semidirect
37. #10622184C22semidirect
39. #10622096C22semidirect
40. #10622095C22semidirect
146. C2×#486D11semidirect
354. C11#19196semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130795342
#130773292
#130681462
#130680222
#130673642
#130672972
#130672842
C2×C11×#4862
#1919611