Finite Group Databasebeta

← #14676279

Subgroups — #14676279

Order 2816.

1794 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic
2C2×#10622259C212yesmaximal
3C2×#10622585C212yesmaximal
4#13066868C212yesmaximal
5#13066866C212yesmaximal
6Dic11⋊#95C211yesmaximal, characteristic
7Dic11⋊#95C211yesmaximal, characteristic
8#13066843C211yesmaximal, characteristic
9#13066841C211yesmaximal, characteristic
10#95×Dic11C211yesmaximal, characteristic
11C11×C4⋊#95C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×C4×Dic22—28no—
24C2×C4×Dic22C418yescomplemented
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622585—28no—
38#10622259—28no—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×Dic22—24no—
51C22×Dic22—24no—
52C22×Dic22C2×C414yes—
53C22×Dic22D414yes—
54C22×Dic22Q814yes—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—42no—
58C2×C42×C11—24no—
59C2×C42×C11C2×C414yes—
60C2×C4⋊Dic11—24no—
61C2×C4⋊Dic11C2×C414yes—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—24no—
66C2×Dic11⋊C4—24no—
67C2×Dic11⋊C4—24no—
68C2×Dic11⋊C4—42no—
69C2×Dic11⋊C4C2×C414yes—
70C2×Dic11⋊C4C2×C414yes—
71C2×Dic11⋊C4D418yes—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11C2×C414yes—
78C2×C4×Dic11C2×C414yes—
79C4×Dic22—232no—
80C11×#95—24no—
81C11×#95—22no—
82C11×#95—22no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—22no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—42no—
91C11⋊#95Q814yescomplemented
92#13935—111nomaximal, Sylow
93C24×C11C2411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
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×C11—22no—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C2×D414yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×Q812yes—
120C22×C4×C11C2×Q812yes—
121C22×C4×C11#4114yes—
122C22×C4×C11#4112yes—
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—21no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11C22×C412yes—
146C22×Dic11C22×C412yes—
147C22×Dic11C22×C412yes—
148C22×Dic11C22×C412yes—
149C22×Dic11C2×D414yes—
150C22×Dic11C2×D412yes—
151C22×Dic11C2×D414yes—
152C22×Dic11C2×D412yes—
153C22×Dic11C2×Q814yes—
154C22×Dic11C2×Q812yes—
155C22×Dic11C2×Q812yes—
156C22×Dic11#4114yes—
157C2×Dic22—28no—
158C2×Dic22—28no—
159C2×Dic22—216no—
160C2×Dic22—216no—
161C2×Dic22C4⋊C4116yescomplemented
162C11×C4⋊C4—48no—
163C42×C11—28no—
164C4⋊Dic11—28no—
165Dic11⋊C4—28no—
166Dic11⋊C4—48no—
167Dic11⋊C4—48no—
168Dic11⋊C4C22⋊C4116yes—
169C4×Dic11—28no—
170C4×Dic11—28no—
171C4×Dic11—48no—
172C22×C4×Q8—111no—
173C2×#391—112no—
174C2×#389—112no—
175#1441—112no—
176#1441—112no—
177C4⋊#95—111no—
178C4⋊#95—111no—
179C4⋊#95D1111yescharacteristic
180#1434—111no—
181#1434—111no—
182C4×#95—111no—
183C23×C11C23×C411yescharacteristic
184C23×C11C22×D412yes—
185C23×C11C22×D411yescharacteristic
186C23×C11C22×Q811yescharacteristic
187C23×C11C22×Q811yescharacteristic
188C23×C11C2×#4112yes—
189C23×C11C2×#4111yescharacteristic
190C23×C11C2×#4112yes—
191C23×C11H(5,𝔽2)11yescharacteristic
192C23×C112−1+411yescharacteristic
193C23×C112−1+412yes—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11C2×C22⋊C414yes—
221C2×C4×C11C2×C4⋊C414yes—
222C2×C4×C11C4×Q814yes—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11C2×C22⋊C414yes—
251C2×Dic11C2×C22⋊C414yes—
252C2×Dic11C2×C4⋊C414yes—
253C2×Dic11C2×C4⋊C414yes—
254C2×Dic11#11714yes—
255C2×Dic11#12118yes—
256C2×Dic11C22⋊Q818yes—
257Dic22—232no—
258C23×Q8—111no—
259C2×C4×Q8—118no—
260C2×C4×Q8—228no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4C2×D1112yes—
267C22×C42—111no—
268C22×C42—111no—
269C22×C42—112no—
270C22×C42C2×D1111yescharacteristic
271#391—228no—
272#389—228no—
273C2×#95—111no—
274C2×#95—112no—
275C2×#95—111no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—112no—
282C2×#95C2×D1111yescharacteristic
283C2×#95C2×D1111yescharacteristic
284C2×#95C2×D1112yes—
285C22×C11C22×C22⋊C411yescharacteristic
286C22×C11C22×C4⋊C411yescharacteristic
287C22×C11C2×#11711yescharacteristic
288C22×C11C2×C4×Q811yescharacteristic
289C22×C11C4×#4111yescharacteristic
290C22×C11#51911yescharacteristic
291C22×C11#52011yescharacteristic
292C22×C11C2×#12112yes—
293C22×C11C2×C22⋊Q812yes—
294C22×C11#52912yes—
295C22×C11#53312yes—
296C22×C11#54112yes—
297C22×C11#54212yes—
298C22×C11#54612yes—
299C22×C11#54712yes—
300C22×C11#54812yes—
301C22×C11#54812yes—
302C22×C11D4×Q811yescharacteristic
303C22×C11D4×Q812yes—
304C22×C11#55011yescharacteristic
305C22×C11#55711yescharacteristic
306C22×C11#55712yes—
307C22×C11Q8211yescharacteristic
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—24no—
311C4×C11—44no—
312C4×C11—82no—
313Dic11—24no—
314Dic11—24no—
315Dic11—42no—
316Dic11—44no—
317Dic11—82no—
318Dic11#38018yes—
319C22×Q8—114no—
320C22×Q8—114no—
321C22×Q8—114no—
322C22×Q8—224no—
323C22×Q8—224no—
324C23×C4—111no—
325C23×C4—111no—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4—112no—
329C23×C4—112no—
330C23×C4C22×D1112yes—
331C23×C4C22×D1112yes—
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1111yescharacteristic
335C4×Q8—2232no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—224no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4—224no—
348C2×C4⋊C4—224no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—442no—
351C2×C42—24no—
352C2×C42—114no—
353C2×C42—114no—
354C2×C42—224no—
355C2×C42—224no—
356C2×C42—224no—
357C2×C42—224no—
358C2×C42—224no—
359C2×C42C4×D1114yes—
360#95—24no—
361#95—22no—
362#95—22no—
363#95—114no—
364#95—224no—
365#95—224no—
366#95—224no—
367#95—224no—
368#95—224no—
369#95—224no—
370#95—222no—
371#95—442no—
372C2×C11C2×#38011yescharacteristic
373C2×C11#229511yescharacteristic
374C2×C11#232011yescharacteristic
375C2×C11#233911yescharacteristic
376C2×C11Q8×C22⋊C411yescharacteristic
377C2×C11Q8×C4⋊C411yescharacteristic
378C2×C11#235111yescharacteristic
379C2×C11#242612yes—
380C2×C11#242912yes—
381C2×C11#245112yes—
382C2×C11#245312yes—
383C24C23×D1111yescharacteristic
384C2×Q8—1116no—
385C2×Q8—228no—
386C2×Q8—228no—
387C2×Q8—2216no—
388C2×Q8—2216no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—112no—
410C22×C4—114no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—114no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—114no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—221no—
432C22×C4—222no—
433C22×C4—221no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4C2×C4×D1112yes—
444C22×C4C2×C4×D1112yes—
445C22×C4C2×C4×D1112yes—
446C22×C4#433914yes—
447C22×C4D4×D1114yes—
448C22×C4D4×D1112yes—
449C22×C4#434112yes—
450C22×C4Q8×D1112yes—
451C22×C4Q8×D1112yes—
452C4⋊C4—48no—
453C4⋊C4—1116no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—448no—
457C4⋊C4—448no—
458C42—28no—
459C42—228no—
460C42—228no—
461C42—448no—
462C11#1393511yescharacteristic, complemented, Sylow
463C23C22×C4×D1111yescharacteristic
464C23C2×#433912yes—
465C23C2×D4×D1111yescharacteristic
466C23C2×D4×D1112yes—
467C23C2×#434111yescharacteristic
468C23#6703711yescharacteristic
469C23C2×Q8×D1111yescharacteristic
470C23C2×Q8×D1111yescharacteristic
471C23#6704011yescharacteristic
472C23#41×D1112yes—
473C23#6704312yes—
474Q8—2232no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—114no—
502C2×C4—114no—
503C2×C4—114no—
504C2×C4—118no—
505C2×C4—118no—
506C2×C4—114no—
507C2×C4—114no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4C22⋊C4×D1114yes—
536C2×C4#6694014yes—
537C2×C4C4⋊C4×D1114yes—
538C22C4×#433911yescharacteristic
539C22C2×C22⋊C4×D1111yescharacteristic
540C22#1062302112yes—
541C22C2×#6694011yescharacteristic
542C22C2×C4⋊C4×D1111yescharacteristic
543C22#1062303511yescharacteristic
544C22#1062303812yes—
545C22#1062304711yescharacteristic
546C22D11×#11711yescharacteristic
547C22#1062306912yes—
548C22#1062308312yes—
549C22#1062309812yes—
550C22#1062310912yes—
551C22#1062312912yes—
552C22D11×#12112yes—
553C22D11×C22⋊Q812yes—
554C22#1062316312yes—
555C22#1062320012yes—
556C22#1062322712yes—
557C22#1062324911yescharacteristic
558C22#1062325211yescharacteristic
559C22#1062325311yescharacteristic
560C22#1062325811yescharacteristic
561C4—24no—
562C4—24no—
563C4—24no—
564C4—44no—
565C4—82no—
566C4—118no—
567C4—224no—
568C4—224no—
569C4—442no—
570C4—444no—
571C4—882no—
572C2D11×#38011yescharacteristic
573C2#1307109211yescharacteristic
574C2#1307126411yescharacteristic
575C2#1307144311yescharacteristic
576C2#1307144811yescharacteristic
577C2#1307152811yescharacteristic
578C2#1307153611yescharacteristic
579C2#1307217912yes—
580C2#1307221412yes—
581C2#1307245212yes—
582C2#1307247412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4⋊#95D11
hypocenterC11#13935
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
24. C2×C4×Dic22C4semidirect
91. C11⋊#95Q8semidirect
161. C2×Dic22C4⋊C4semidirect
462. C11#13935semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C2×#106222592
C2×#106225852
#130668682
#130668662
Dic11⋊#952
#130668432
#130668412
#95×Dic112
C11×C4⋊#952
#1393511