Finite Group Databasebeta

← #14649596

Subgroups — #14649596

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078707C211yesmaximal, characteristic
2#13068441C211yesmaximal, characteristic, complemented
3#13067228C211yesmaximal, characteristic, complemented
4#13067112C211yesmaximal, characteristic, complemented
5#13066516C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#2974C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#436—21no—
11C11×#435—22no—
12C8×D4×C11—21no—
13C11×#432C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#407—21no—
16C2×C11×C22⋊C8—21no—
17#10622830—21no—
18C2×#66896—21no—
19#10622628C411yescharacteristic, complemented
20#10622628C411yescharacteristic, complemented
21#10622627—21no—
22#10622627—21no—
23#10622621C411yescharacteristic, complemented
24#10622621C411yescharacteristic, complemented
25#10622581—21no—
26C4×C4⋊Dic11C2211yescharacteristic
27#10622539C2211yescharacteristic
28C2×#66867C2211yescharacteristic
29#10622167—21no—
30#10622108—21no—
31#10622108—21no—
32#10622102—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×#4339—21no—
36C2×C11×M16—22no—
37C22×C8×C11—22no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11C2×C411yescharacteristic
41C4×D4×C11C2×C411yescharacteristic
42C4×D4×C11D411yescharacteristic
43C4×D4×C11D411yescharacteristic
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4323—21no—
48C2×#4323—21no—
49#66983—21no—
50#66983—21no—
51C2×C4⋊Dic11—21no—
52C2×C4×Dic11—21no—
53C22×C11⋊C8—21no—
54#66928—21no—
55#66927C2×C411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922C2×C411yescharacteristic
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C22⋊C8—22no—
62C11×C22⋊C8—22no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8D411yescharacteristic
65C11×C22⋊C8D411yescharacteristic
66C11×#97D412yes—
67C4×C8×C11—21no—
68#66896—24no—
69#66896—21no—
70#66896—21no—
71C11⋊#95—21no—
72C22⋊(C11⋊C8)—21no—
73#66873—21no—
74#66873—21no—
75#66872—21no—
76#66872—21no—
77C4⋊(C11⋊C8)C2×C411yescharacteristic
78C4⋊(C11⋊C8)C2×C411yescharacteristic
79#66867—21no—
80#66867—21no—
81#66867—21no—
82#9163—111nomaximal, Sylow
83C24×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C2×D4×C11C22⋊C411yescharacteristic
88C2×D4×C11C22⋊C411yescharacteristic
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—82no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C2×C22⋊D11—41no—
99C22×Dic11—41no—
100#4339—81no—
101#4339—81no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×C4×D11—41no—
106C2×Dic22—21no—
107C11×M16—82no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—22no—
111C2×C8×C11—82no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4C22⋊C411yescharacteristic
114C11×C4⋊C4C22⋊C411yescharacteristic
115C11×C22⋊C4—21no—
116C11×C22⋊C4—21no—
117C11×C22⋊C4—21no—
118C11×C22⋊C4—21no—
119C42×C11C22×C411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123#4323—42no—
124#4323—42no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—22no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—41no—
131C4×Dic11—81no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137#3109—111no—
138#2974D1111yescharacteristic, complemented
139#1762—111no—
140#1530—111no—
141#1502—111no—
142#1302—111no—
143#1285—111no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—42no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—81no—
150C23×C11#12111yescharacteristic
151C22×D11—41no—
152D4×C11—21no—
153D4×C11—21no—
154D4×C11—21no—
155D4×C11—42no—
156D4×C11#10412yes—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11C2×C22⋊C411yescharacteristic
170C2×C4×C11C4×D411yescharacteristic
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12311yescharacteristic
175C22⋊D11—81no—
176C22⋊D11—81no—
177C2×Dic11—42no—
178C2×Dic11—41no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181D44—41no—
182D44—41no—
183D44—81no—
184D44—81no—
185C4×D11—82no—
186Dic22—81no—
187C8×C11—41no—
188C8×C11—42no—
189C8×C11—41no—
190C11⋊C8—42no—
191C11⋊C8—41no—
192C11⋊C8—41no—
193#532—111no—
194C2×C4×D4C2×D1111yescharacteristic
195#481—221no—
196#476—111no—
197#476—111no—
198#459—111no—
199#459—111no—
200#447—221no—
201#442—221no—
202#442—221no—
203#436—21no—
204#435—22no—
205C8×D4—21no—
206#432—111no—
207#432C2×D1111yescharacteristic
208#431C2×D1111yescharacteristic
209C2×#102—221no—
210#407—21no—
211C2×C22⋊C8—21no—
212C2×#97—111no—
213C4×C4⋊C4—111no—
214#340—221no—
215#329—222no—
216#327—221no—
217#327—221no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—22no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11#38611yescharacteristic
229C22×C11#47111yescharacteristic
230C22×C11#47211yescharacteristic
231C2×D11—81no—
232C2×D11—81no—
233C2×D11—81no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11C2×#10411yescharacteristic
242C4×C11#42111yescharacteristic
243Dic11—82no—
244Dic11—81no—
245C2×#41—221no—
246C22×D4D4411yescharacteristic
247C23×C4—21no—
248C2×D8—221no—
249C2×D8—221no—
250C2×M16—22no—
251C22×C8—22no—
252C22×C8—221no—
253C4⋊Q8—111no—
254#127—111no—
255#124—221no—
256#121—221no—
257#121—221no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—221no—
261C4×D4—221no—
262C4×D4C4×D1111yescharacteristic
263C4×D4C4×D1111yescharacteristic
264C4×D4C22⋊D1111yescharacteristic
265C4×D4C22⋊D1111yescharacteristic
266C2×C4⋊C4—221no—
267C2×C4⋊C4D4411yescharacteristic
268C2×C22⋊C4—21no—
269C2×C42—221no—
270C2×C42C22×D1111yescharacteristic
271#106—221no—
272#106—221no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—111no—
276C4⋊C8—111no—
277#102—224no—
278#102—221no—
279#102—221no—
280#102—221no—
281#102—221no—
282C22⋊C8—22no—
283C22⋊C8—22no—
284C22⋊C8—21no—
285C22⋊C8—221no—
286C22⋊C8C22⋊D1111yescharacteristic
287C22⋊C8C22⋊D1111yescharacteristic
288#97—221no—
289#97—221no—
290#97—221no—
291#97C22⋊D1112yes—
292C4×C8—21no—
293#95—221no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—42no—
297C2×C11—81no—
298C2×C11#187111yescharacteristic
299C2×C11#190411yescharacteristic
300C2×C11#190711yescharacteristic
301D11—161no—
302C24—21no—
303#41—881no—
304#41—881no—
305C2×Q8—221no—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4—41no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—441no—
313C2×D4(C2×D11)⋊C411yescharacteristic
314C2×D4(C2×D11)⋊C411yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—82no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4C2×D4411yescharacteristic
324C22×C4#433911yescharacteristic
325C22×C4C2×C22⋊D1111yescharacteristic
326D8—442no—
327D8—442no—
328M16—82no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—22no—
332C2×C8—82no—
333C2×C8—222no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—441no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—222no—
340C4⋊C4—221no—
341C4⋊C4—221no—
342C4⋊C4—441no—
343C4⋊C4(C2×D11)⋊C411yescharacteristic
344C4⋊C4(C2×D11)⋊C411yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—441no—
350C22⋊C4—441no—
351C42—881no—
352C42C2×C4×D1111yescharacteristic
353C42#433911yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C42C2×C22⋊D1111yescharacteristic
356C11#916311yescharacteristic, complemented, Sylow
357C23—21no—
358C23—21no—
359C23—42no—
360C23—41no—
361C23—41no—
362C23—81no—
363C23—441no—
364C23#6698311yescharacteristic
365Q8—881no—
366D4—21no—
367D4—21no—
368D4—21no—
369D4—42no—
370D4—441no—
371D4—441no—
372D4—881no—
373D4—881no—
374D4—881no—
375D4—881no—
376D4#6688912yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—442no—
390C2×C4—441no—
391C2×C4—882no—
392C2×C4—881no—
393C2×C4—881no—
394C2×C4C2×(C2×D11)⋊C411yescharacteristic
395C2×C4C4×C22⋊D1111yescharacteristic
396C2×C4C4×C22⋊D1111yescharacteristic
397C2×C4#6698211yescharacteristic
398C2×C4#6698311yescharacteristic
399C2×C4#6700611yescharacteristic
400C8—41no—
401C8—42no—
402C8—41no—
403C8—442no—
404C8—441no—
405C8—441no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22—82no—
416C22—881no—
417C22—881no—
418C22—881no—
419C22#1062275411yescharacteristic
420C22#1062275511yescharacteristic
421C22#1062282611yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—882no—
430C4—881no—
431C4C2×#6688911yescharacteristic
432C4#1062275211yescharacteristic
433C2—21no—
434C2—21no—
435C2—42no—
436C2—81no—
437C2—1761no—
438C2#1306891811yescharacteristic
439C2#1306910311yescharacteristic
440C2#1306912411yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2974C2
socleC22×C11#386
prime radical#13078707C2
cosocleC2×C42×C11C23
hypercenter#2974D11
hypocenterC11#9163
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13068441C2semidirect
3. #13067228C2semidirect
4. #13067112C2semidirect
5. #13066516C2semidirect
6. #13066471C2semidirect
7. C11×#2974C2semidirect
19. #10622628C4semidirect
20. #10622628C4semidirect
23. #10622621C4semidirect
24. #10622621C4semidirect
138. #2974D11semidirect
356. C11#9163semidirect

Maximal subgroups

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

subgroupindex
#130787072
#130684412
#130672282
#130671122
#130665162
#130664712
C11×#29742
#916311