Finite Group Databasebeta

← #14803322

Subgroups — #14803322

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622629C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13074104C211yesmaximal, characteristic, complemented
4#13070008C211yesmaximal, characteristic, complemented
5#13069987C211yesmaximal, characteristic, complemented
6#13069933C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic
8#13069481C211yesmaximal, characteristic
9#13069469C211yesmaximal, characteristic, complemented
10#13069425C211yesmaximal, characteristic, complemented
11#13069382C211yesmaximal, characteristic, complemented
12#13069298C211yesmaximal, characteristic, complemented
13#13069291C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2580C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×#4324C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×#66928C2211yescharacteristic
21C11×#399—21no—
22C11×#393—21no—
23C11×#390C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#385—21no—
28C11×#385—21no—
29C11×#382C2211yescharacteristic
30#10622844—21no—
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33Q8×C11⋊C8—24no—
34#10622629—24no—
35#10622606—21no—
36#10622603—21no—
37#10622603—21no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622552C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11D411yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×D44C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×#4324—22no—
87C2×#4324—22no—
88C2×#4324—41no—
89C2×#4323—22no—
90C2×#4323—22no—
91C2×#4323—41no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66928—22no—
106#66928—22no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111#66896—22no—
112#66896—22no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66874—22no—
119#66874—22no—
120#66874—41no—
121#66873—22no—
122#66873—22no—
123#66873—41no—
124#66872—41no—
125#66871—41no—
126C4⋊(C11⋊C8)—22no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)D414yes—
129C4×C11⋊C8—22no—
130C4×C11⋊C8—22no—
131C4×C11⋊C8—22no—
132#25296—111nomaximal, Sylow
133C24×C11—21no—
134C23×D11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11#4112yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4—81no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—81no—
187C11×C22⋊C4—81no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11C2×D412yes—
193C42×C11#4112yes—
194#4324—44no—
195#4323—44no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—81no—
201(C2×D11)⋊C4—81no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4×Dic11—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8C2×D412yes—
218C2×C11⋊C8#4112yes—
219C2×#463—111no—
220C2×C8×Q8—111no—
221#2592—111no—
222#2580D1111yescharacteristic, complemented
223#2068—111no—
224#2065—111no—
225#2055—111no—
226#2054—111no—
227#1970—111no—
228#1968—111no—
229#1958—111no—
230#1949—111no—
231#1934—111no—
232#1933—111no—
233C4×#102—111no—
234C23×C11—22no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11C22×D411yescharacteristic
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249Q8×C11—28no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—41no—
253D4×C11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—84no—
278C2×C4×C11#12112yes—
279C2×C4×C11#12112yes—
280C2×C4×C11#13512yes—
281C2×C4×C11#13512yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297D44—41no—
298D44—41no—
299D44—41no—
300D44—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304Dic22—41no—
305C11⋊C8—22no—
306C11⋊C8—22no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C22×SD16—111no—
310C22×D8—111no—
311C2×#124—111no—
312C2×C4×Q8C2×D1111yescharacteristic
313C2×C4×D4C2×D1111yescharacteristic
314#463—224no—
315C8×Q8—224no—
316C2×#107—111no—
317C2×#106—111no—
318C2×C4⋊C8—111no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×C4×C8—111no—
330C2×C4×C8—111no—
331C2×C4×C8—111no—
332#399—21no—
333#397—221no—
334#393—21no—
335#393—221no—
336#391—111no—
337#391—111no—
338#390—111no—
339#390—111no—
340#390C2×D1111yescharacteristic
341#390C2×D1111yescharacteristic
342#389C2×D1111yescharacteristic
343#389C2×D1111yescharacteristic
344#388—221no—
345#388—221no—
346#385—21no—
347#385—21no—
348#382C2×D1111yescharacteristic
349C4×C4⋊C4—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11C2×#12111yescharacteristic
362C22×C11#54811yescharacteristic
363C22×C11#55011yescharacteristic
364C22×C11C2×#13511yescharacteristic
365C22×C11C2×#13511yescharacteristic
366C22×C11#57611yescharacteristic
367C22×C11#57711yescharacteristic
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11#52911yescharacteristic
385C4×C11#54211yescharacteristic
386C4×C11#54611yescharacteristic
387C4×C11#54811yescharacteristic
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—111no—
392C22×Q8C22⋊D1111yescharacteristic
393C22×D4—111no—
394C22×D4C22×D1111yescharacteristic
395C23×C4—21no—
396C2×SD16—222no—
397C2×SD16—222no—
398C2×SD16—441no—
399C2×D8—222no—
400C2×D8—222no—
401C2×D8—441no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—111no—
405C22×C8—111no—
406#124—222no—
407#124—222no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×D4—22no—
411C4×D4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4C22⋊D1111yescharacteristic
417C2×C4⋊C4C22⋊D1111yescharacteristic
418C2×C4⋊C4C22⋊D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437#107—441no—
438#106—441no—
439C4⋊C8—114no—
440C4⋊C8—222no—
441C4⋊C8—222no—
442#103—222no—
443#103—222no—
444#103—441no—
445#102—222no—
446#102—222no—
447#102—222no—
448#102—222no—
449#102—441no—
450C4×C8—222no—
451C4×C8—222no—
452C4×C8—222no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11—82no—
463C2×C11#242611yescharacteristic
464C2×C11#305011yescharacteristic
465C2×C11#306211yescharacteristic
466C2×C11#336011yescharacteristic
467C2×C11#336111yescharacteristic
468C2×C11#339411yescharacteristic
469C2×C11#339611yescharacteristic
470D11—161no—
471C24—21no—
472C24—221no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4#434312yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510SD16—444no—
511D8—444no—
512C2×C8—112no—
513C2×C8—112no—
514C2×C8—112no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—81no—
534C4⋊C4—81no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—81no—
543C22⋊C4—81no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—881no—
549C22⋊C4—881no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—881no—
555C42D4×D1112yes—
556C42#434112yes—
557C11#2529611yescharacteristic, complemented, Sylow
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23C22×C22⋊D1111yescharacteristic
573Q8—28no—
574Q8—441no—
575Q8—441no—
576Q8—441no—
577Q8—441no—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582D4—441no—
583D4—441no—
584D4—441no—
585D4—441no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4#6699212yes—
620C2×C4#6699212yes—
621C2×C4#6700312yes—
622C2×C4#6700312yes—
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4C2×#434311yescharacteristic
626C2×C4#6704011yescharacteristic
627C2×C4#41×D1111yescharacteristic
628C2×C4#6704211yescharacteristic
629C8—222no—
630C8—222no—
631C8—222no—
632C8—441no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22—881no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22C2×#6699211yescharacteristic
648C22#1062334811yescharacteristic
649C22C2×#6700311yescharacteristic
650C22C2×#6700311yescharacteristic
651C22#1062336511yescharacteristic
652C22#1062336611yescharacteristic
653C22#1062336711yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—881no—
664C4—881no—
665C4—881no—
666C4#1062315511yescharacteristic
667C4#1062316111yescharacteristic
668C4#1062316411yescharacteristic
669C4#1062317411yescharacteristic
670C2—82no—
671C2—1761no—
672C2#1307218411yescharacteristic
673C2#1307819411yescharacteristic
674C2#1307829211yescharacteristic
675C2#1308126511yescharacteristic
676C2#1308127611yescharacteristic
677C2#1308160811yescharacteristic
678C2#1308162411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2580C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2580D11
hypocenterC11#25296
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2580

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13074104C2semidirect
4. #13070008C2semidirect
5. #13069987C2semidirect
6. #13069933C2semidirect
9. #13069469C2semidirect
10. #13069425C2semidirect
11. #13069382C2semidirect
12. #13069298C2semidirect
13. #13069291C2semidirect
14. C4×#66896C2semidirect
15. C11×#2580C2semidirect
222. #2580D11semidirect
557. C11#25296semidirect

Maximal subgroups

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

subgroupindex
C2×#106226292
C2×Q8×C11⋊C82
#130741042
#130700082
#130699872
#130699332
#130699262
#130694812
#130694692
#130694252
#130693822
#130692982
#130692912
C4×#668962
C11×#25802
#2529611