Finite Group Databasebeta

← #14682285

Subgroups — #14682285

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic
2C2×#10622259C212yesmaximal
3#13066887C211yesmaximal, characteristic
4#13066867C212yesmaximal
5#13066867C212yesmaximal
6#13066847C212yesmaximal
7#13066847C212yesmaximal
8#13066840C212yesmaximal
9C11×#1446C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C2×#66997—28no—
13C2×#66997C418yescomplemented
14C22×Dic11⋊C4C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×Dic11⋊C4C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C2×C11×#95C2212yes—
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33#10622259—28no—
34C22×Q8×C11—24no—
35C22×Q8×C11—42no—
36C22×Q8×C11—41no—
37C22×Q8×C11—41no—
38C22×Q8×C11C2×C414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C22×Dic22—41no—
49C22×Dic22—42no—
50C22×Dic22—41no—
51C22×Dic22C2×C414yes—
52C22×Dic22D418yes—
53#66997—232no—
54C2×Dic11⋊C4—24no—
55C2×Dic11⋊C4—24no—
56C2×Dic11⋊C4—24no—
57C2×Dic11⋊C4—24no—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4—42no—
60C2×Dic11⋊C4—42no—
61C2×Dic11⋊C4C2×C418yes—
62C2×Dic11⋊C4C2×C418yes—
63C2×C4×Dic11—24no—
64C2×C4×Dic11—24no—
65C2×C4×Dic11—42no—
66C2×C4×Dic11—42no—
67C2×C4×Dic11C2×C414yes—
68C11×#95—24no—
69C11×#95—41no—
70C11×#95—42no—
71C11×#95—41no—
72C11⋊#95—24no—
73C11⋊#95—24no—
74C11⋊#95—24no—
75C11⋊#95—24no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—41no—
79C11⋊#95—42no—
80C11⋊#95—41no—
81C11⋊#95Q818yescomplemented
82#14450—111nomaximal, Sylow
83C24×C11C2411yescharacteristic
84C2×Q8×C11—28no—
85C2×Q8×C11—44no—
86C2×Q8×C11—44no—
87C2×Q8×C11—48no—
88C2×Q8×C11—48no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C2×D414yes—
117C22×C4×C11C2×Q814yes—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11C22×C414yes—
140C22×Dic11C22×C414yes—
141C22×Dic11C2×D414yes—
142C22×Dic11C2×D414yes—
143C22×Dic11C2×Q814yes—
144C22×Dic11C2×Q814yes—
145C22×Dic11#4114yes—
146C2×Dic22—44no—
147C2×Dic22—44no—
148C2×Dic22—48no—
149C2×Dic22—48no—
150C2×Dic22C22⋊C4116yes—
151Dic11⋊C4—216no—
152Dic11⋊C4—216no—
153Dic11⋊C4—48no—
154C4×Dic11—28no—
155C4×Dic11—48no—
156C22×C4⋊Q8—111no—
157C2×#391—112no—
158#1446—111no—
159#1446D1111yescharacteristic
160#1441—112no—
161#1441—112no—
162#1436—112no—
163#1436—112no—
164#1434—112no—
165C23×C11C23×C411yescharacteristic
166C23×C11C22×D412yes—
167C23×C11C22×Q812yes—
168C23×C11C2×#4112yes—
169C23×C11H(5,𝔽2)12yes—
170C23×C11H(5,𝔽2)11yescharacteristic
171C23×C11H(5,𝔽2)11yescharacteristic
172C23×C112−1+412yes—
173C23×C112−1+412yes—
174Q8×C11—416no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11C2×C22⋊C414yes—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11C2×C22⋊C418yes—
231C2×Dic11C4×Q818yes—
232Dic22—416no—
233C23×Q8—111no—
234C23×Q8C2×D1111yescharacteristic
235C2×C4⋊Q8—118no—
236C2×C4⋊Q8—228no—
237C22×C4⋊C4—112no—
238C22×C4⋊C4—112no—
239C22×C4⋊C4—112no—
240C22×C42—111no—
241C22×C42—112no—
242#391—228no—
243C2×#95—112no—
244C2×#95—112no—
245C2×#95—112no—
246C2×#95—112no—
247C2×#95—112no—
248C2×#95—112no—
249C2×#95—112no—
250C2×#95—111no—
251C2×#95—112no—
252C2×#95—111no—
253C2×#95C2×D1112yes—
254C2×#95C2×D1111yescharacteristic
255C2×#95C2×D1112yes—
256C2×#95C2×D1111yescharacteristic
257C22×C11C22×C22⋊C411yescharacteristic
258C22×C11C2×C4×Q812yes—
259C22×C11#51811yescharacteristic
260C22×C11#51811yescharacteristic
261C22×C11#51912yes—
262C22×C11#53412yes—
263C22×C11#53412yes—
264C22×C11#54212yes—
265C22×C11#54212yes—
266C22×C11#54412yes—
267C22×C11#54412yes—
268C22×C11#54812yes—
269C22×C11#54812yes—
270C22×C11D4×Q812yes—
271C22×C11D4×Q812yes—
272C22×C11#55412yes—
273C22×C11#55511yescharacteristic
274C22×C11Q8211yescharacteristic
275C22×C11#56311yescharacteristic
276C22×C11#56312yes—
277C22×C11#56311yescharacteristic
278C4×C11—24no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—44no—
282C4×C11—82no—
283Dic11—28no—
284Dic11—28no—
285Dic11—44no—
286Dic11—82no—
287C22×Q8—24no—
288C22×Q8—41no—
289C22×Q8—42no—
290C22×Q8—41no—
291C22×Q8—114no—
292C22×Q8—118no—
293C22×Q8—441no—
294C22×Q8—442no—
295C22×Q8—441no—
296C22×Q8C4×D1114yes—
297C23×C4—112no—
298C23×C4—112no—
299C23×C4—112no—
300C23×C4—112no—
301C23×C4C22×D1112yes—
302C23×C4C22×D1111yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C23×C4C22×D1112yes—
305C23×C4C22×D1111yescharacteristic
306C4⋊Q8—2232no—
307C2×C4⋊C4—118no—
308C2×C4⋊C4—118no—
309C2×C4⋊C4—224no—
310C2×C4⋊C4—224no—
311C2×C4⋊C4—224no—
312C2×C4⋊C4—224no—
313C2×C4⋊C4—224no—
314C2×C4⋊C4—442no—
315C2×C4⋊C4—442no—
316C2×C42—114no—
317C2×C42—224no—
318C2×C42—224no—
319C2×C42—442no—
320C2×C42—442no—
321#95—24no—
322#95—41no—
323#95—42no—
324#95—41no—
325#95—118no—
326#95—224no—
327#95—224no—
328#95—224no—
329#95—224no—
330#95—224no—
331#95—224no—
332#95—441no—
333#95—442no—
334#95—441no—
335C2×C11#230811yescharacteristic
336C2×C11#233112yes—
337C2×C11Q8×C22⋊C412yes—
338C2×C11#236911yescharacteristic
339C2×C11#238111yescharacteristic
340C2×C11#272912yes—
341C2×C11#272912yes—
342C2×C11#273112yes—
343C2×C11#273412yes—
344C24C23×D1111yescharacteristic
345C2×Q8—28no—
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—48no—
349C2×Q8—48no—
350C2×Q8—1116no—
351C2×Q8—444no—
352C2×Q8—444no—
353C2×Q8—448no—
354C2×Q8—448no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—114no—
380C22×C4—114no—
381C22×C4—114no—
382C22×C4—114no—
383C22×C4—114no—
384C22×C4—114no—
385C22×C4—114no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4C2×C4×D1112yes—
408C22×C4C2×C4×D1112yes—
409C22×C4C2×C4×D1112yes—
410C22×C4D4×D1114yes—
411C22×C4Q8×D1114yes—
412C4⋊C4—2216no—
413C4⋊C4—2216no—
414C4⋊C4—448no—
415C42—228no—
416C42—448no—
417C11#1445011yescharacteristic, complemented, Sylow
418C23C22×C4×D1111yescharacteristic
419C23C2×D4×D1112yes—
420C23#6703711yescharacteristic
421C23#6703712yes—
422C23#6703711yescharacteristic
423C23C2×Q8×D1112yes—
424C23#6704012yes—
425C23#41×D1112yes—
426C23#6704312yes—
427Q8—416no—
428Q8—4416no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—118no—
458C2×C4—118no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—224no—
467C2×C4—224no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4C22⋊C4×D1114yes—
486C22C2×C22⋊C4×D1111yescharacteristic
487C22#1062301711yescharacteristic
488C22#1062301711yescharacteristic
489C22C4×Q8×D1112yes—
490C22#1062310312yes—
491C22#1062312012yes—
492C22#1062312012yes—
493C22#1062315412yes—
494C22#1062316312yes—
495C22#1062316412yes—
496C22#1062316712yes—
497C22#1062317112yes—
498C22#1062317712yes—
499C22#1062320012yes—
500C22#1062320111yescharacteristic
501C22#1062320311yescharacteristic
502C22#1062320812yes—
503C22#1062325311yescharacteristic
504C22#1062325812yes—
505C22#1062326012yes—
506C22#1062326611yescharacteristic
507C4—24no—
508C4—42no—
509C4—42no—
510C4—44no—
511C4—82no—
512C4—228no—
513C4—228no—
514C4—444no—
515C4—882no—
516C2#1307119211yescharacteristic
517C2#1307135912yes—
518C2#1307145012yes—
519C2#1307170411yescharacteristic
520C2#1307179511yescharacteristic
521C2#1307560312yes—
522C2#1307560512yes—
523C2#1307562912yes—
524C2#1307565012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1446D11
hypocenterC11#14450
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
13. C2×#66997C4semidirect
81. C11⋊#95Q8semidirect
417. C11#14450semidirect

Maximal subgroups

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

subgroupindex
C22×#669972
C2×#106222592
#130668872
#130668672
#130668472
#130668402
C11×#14462
#1445011