Finite Group Databasebeta

← #14649525

Subgroups — #14649525

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076900C211yesmaximal, characteristic
2C2×#10622280C211yesmaximal, characteristic
3#13068525C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic, complemented
5#13066496C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C2×C11×#328C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×#66999C412yescomplemented
11C22×(C2×D11)⋊C4—21no—
12C22×Dic11⋊C4—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15#10622825C2211yescharacteristic
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×(C2×D11)⋊C8—22no—
19#10622602—22no—
20#10622600C412yescomplemented
21#10622568—21no—
22#10622559—21no—
23#10622280—22no—
24#10622280—22no—
25C11×#328—22no—
26#10622176—22no—
27C24×D11D411yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C22×C4×D11—21no—
34C22×C4×D11—21no—
35C22×C4×D11—21no—
36C22×C4×D11—21no—
37C22×C4×D11—44no—
38C22×C4×D11C2×C412yes—
39C22×C4×D11D412yes—
40C22×C8×C11—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C22⋊Dic11—21no—
49#66999—44no—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—42no—
54C2×(C2×D11)⋊C4—42no—
55C2×C4⋊Dic11C2×C412yes—
56C2×Dic11⋊C4—24no—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—44no—
59C22×C11⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#95—21no—
63C11×#95D412yes—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—22no—
67C11⋊#95D412yes—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70(C2×D11)⋊C8—44no—
71#9151—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C23×D11—21no—
74C23×D11—21no—
75C23×D11—21no—
76C23×D11—21no—
77C23×D11—42no—
78C23×D11—42no—
79C23×D11C22⋊C412yes—
80C23×D11SD1612yes—
81C23×D11Q1612yes—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—42no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×Dic11—24no—
100C22×Dic11—22no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11—21no—
104C22×Dic11—42no—
105C22×Dic11—42no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11C22⋊C412yes—
109C2×C4×D11—24no—
110C2×C4×D11—24no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×C4×D11—44no—
118C2×C4×D11—44no—
119C2×C4×D11—44no—
120C2×C4×D11—44no—
121C2×C8×C11—42no—
122C2×C8×C11—41no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11—41no—
131(C2×D11)⋊C4—44no—
132(C2×D11)⋊C4—48no—
133(C2×D11)⋊C4—44no—
134C4⋊Dic11—42no—
135Dic11⋊C4—48no—
136Dic11⋊C4—44no—
137C2×C11⋊C8—42no—
138C2×C11⋊C8—41no—
139#2848—111no—
140C2×#380—111no—
141#1779—111no—
142C2×#328—111no—
143C2×#328D1111yescharacteristic, complemented
144#1294—111no—
145#1294—111no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11C2×C22⋊C411yescharacteristic
149C23×C11#12011yescharacteristic
150C23×C11#12311yescharacteristic
151C23×C11C2×SD1611yescharacteristic
152C23×C11C2×Q1611yescharacteristic
153C23×C11AGL(1,ℤ/8)11yescharacteristic
154C23×C11#13711yescharacteristic
155C22×D11—22no—
156C22×D11—22no—
157C22×D11—22no—
158C22×D11—22no—
159C22×D11—22no—
160C22×D11—22no—
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—22no—
164C22×D11—22no—
165C22×D11—44no—
166C22×D11—44no—
167C22×D11—42no—
168C22×D11—42no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—44no—
172C22×D11—44no—
173C22×D11#10314yes—
174Q8×C11—81no—
175Q8×C11—81no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—82no—
190C2×C4×C11—82no—
191C2×C4×C11C4×D411yescharacteristic
192C2×C4×C11C4×D411yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—82no—
206C2×Dic11—82no—
207C2×Dic11#9914yes—
208C4×D11—44no—
209C4×D11—44no—
210C4×D11—44no—
211C4×D11—44no—
212C8×C11—81no—
213C11⋊C8—81no—
214C24×C4—111no—
215C2×C22⋊Q8—112no—
216C2×C22⋊Q8C2×D1111yescharacteristic
217C22×C4⋊C4—221no—
218C22×C22⋊C4—221no—
219C2×C22⋊C8—111no—
220C2×C22⋊C8—222no—
221C2×C22⋊C8C2×D1111yescharacteristic
222#385—221no—
223#385—222no—
224#380—111no—
225#380—112no—
226#380—222no—
227#380—222no—
228#379—221no—
229C2×#95—111no—
230C2×#95C2×D1111yescharacteristic
231#328—22no—
232#328—222no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11#38611yescharacteristic
242C22×C11C2×#9912yes—
243C22×C11C2×#10311yescharacteristic
244C22×C11#41711yescharacteristic
245C22×C11#42112yes—
246C22×C11#45011yescharacteristic
247C22×C11#45111yescharacteristic
248C22×C11#48311yescharacteristic
249C22×C11#48411yescharacteristic
250C2×D11—24no—
251C2×D11—24no—
252C2×D11—24no—
253C2×D11—44no—
254C2×D11—44no—
255C2×D11—44no—
256C2×D11—44no—
257C2×D11—42no—
258C2×D11—42no—
259C2×D11—42no—
260C2×D11—42no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—82no—
266C4×C11—81no—
267C4×C11—81no—
268Dic11—24no—
269Dic11—82no—
270Dic11—82no—
271C25—111no—
272C22×Q8C4×D1111yescharacteristic
273C23×C4—21no—
274C23×C4—111no—
275C23×C4—112no—
276C23×C4—112no—
277C23×C4—221no—
278C23×C4—221no—
279C23×C4—221no—
280C23×C4—221no—
281C23×C4—221no—
282C23×C4—444no—
283C23×C4C22×D1111yescharacteristic
284C22×C8—21no—
285C22×C8—221no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—444no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—224no—
295C2×C4⋊C4—444no—
296C2×C4⋊C4C4×D1111yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—224no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—442no—
303C2×C22⋊C4—442no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—221no—
307C22⋊C8—221no—
308C22⋊C8—444no—
309#95—21no—
310#95—112no—
311#95—222no—
312#95—221no—
313#95—221no—
314#95C22⋊D1112yes—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—21no—
319C2×C11#151312yes—
320C2×C11#152012yes—
321C2×C11#187211yescharacteristic
322C2×C11#189711yescharacteristic
323C2×C11#189811yescharacteristic
324D11—44no—
325C24—112no—
326C24—112no—
327C24—112no—
328C24—221no—
329C24—221no—
330C24—221no—
331C24—221no—
332C24—442no—
333C24—442no—
334C24D4×D1111yescharacteristic
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—42no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—112no—
347C22×C4—224no—
348C22×C4—224no—
349C22×C4—224no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—442no—
359C22×C4—442no—
360C22×C4—444no—
361C22×C4—444no—
362C22×C4—444no—
363C22×C4—444no—
364C22×C4—442no—
365C22×C4—442no—
366C22×C4—441no—
367C22×C4—441no—
368C22×C4C2×C4×D1111yescharacteristic
369C22×C4#433911yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4D4×D1111yescharacteristic
372C22×C4#434111yescharacteristic
373C22×C4C2×C22⋊D1111yescharacteristic
374C2×C8—42no—
375C2×C8—41no—
376C2×C8—442no—
377C2×C8—441no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—442no—
383C4⋊C4—444no—
384C4⋊C4—448no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—448no—
388C22⋊C4—444no—
389C22⋊C4—444no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C11#915111yescharacteristic, complemented, Sylow
393C23—22no—
394C23—22no—
395C23—114no—
396C23—222no—
397C23—222no—
398C23—222no—
399C23—222no—
400C23—222no—
401C23—222no—
402C23—222no—
403C23—222no—
404C23—222no—
405C23—222no—
406C23—444no—
407C23—444no—
408C23—442no—
409C23—442no—
410C23—442no—
411C23—442no—
412C23—444no—
413C23—444no—
414C23C22⋊C4×D1111yescharacteristic
415C23#6693611yescharacteristic
416C23SD16×D1111yescharacteristic
417C23#6696711yescharacteristic
418C23Q16×D1111yescharacteristic
419C23#6697111yescharacteristic
420C23#6699011yescharacteristic
421Q8—81no—
422Q8—81no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—114no—
439C2×C4—224no—
440C2×C4—224no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—444no—
444C2×C4—444no—
445C2×C4—444no—
446C2×C4—444no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—882no—
454C2×C4—882no—
455C2×C4(C22⋊D11)⋊C411yescharacteristic
456C2×C4#6693711yescharacteristic
457C2×C4C4×C22⋊D1111yescharacteristic
458C2×C4#6699111yescharacteristic
459C8—81no—
460C8—881no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—224no—
470C22—224no—
471C22—224no—
472C22—444no—
473C22—444no—
474C22—444no—
475C22—444no—
476C22—442no—
477C22—442no—
478C22—442no—
479C22—442no—
480C22D11×#9912yes—
481C22D11×#10311yescharacteristic
482C22#1062241611yescharacteristic
483C22#1062241811yescharacteristic
484C22#1062242211yescharacteristic
485C22#1062243412yes—
486C22#1062256911yescharacteristic
487C22#1062278211yescharacteristic
488C22#1062279911yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—82no—
494C4—81no—
495C4—81no—
496C4—224no—
497C4—882no—
498C4—882no—
499C2—21no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—444no—
504C2#1306715812yes—
505C2#1306718612yes—
506C2#1306892011yescharacteristic
507C2#1306906111yescharacteristic
508C2#1306906611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenterC2×#328D11
hypocenterC11#9151
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. C2×#10622176C2semidirect
5. #13066496C2semidirect
6. #13066495C2semidirect
7. C2×C11×#328C2semidirect
10. C2×#66999C4semidirect
20. #10622600C4semidirect
143. C2×#328D11semidirect
392. C11#9151semidirect

Maximal subgroups

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

subgroupindex
#130769002
C2×#106222802
#130685252
C2×#106221762
#130664962
#130664952
C2×C11×#3282
#915111