Finite Group Databasebeta

← #14661671

Subgroups — #14661671

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071228C211yesmaximal, characteristic
2#13071228C211yesmaximal, characteristic
3C2×#10622164C211yesmaximal, characteristic
4C2×#10622164C211yesmaximal, characteristic
5C2×#10622165C211yesmaximal, characteristic
6C2×#10622165C211yesmaximal, characteristic
7C2×C11×#342C211yesmaximal, characteristic
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C22⋊Dic11C2211yescharacteristic
12C22×C22⋊Dic11C2211yescharacteristic
13C22×C22⋊Dic11C2211yescharacteristic
14C22×C22⋊Dic11C2211yescharacteristic
15#10622823—22no—
16#10622823C414yescomplemented
17#10622559—22no—
18#10622559—22no—
19#10622555—22no—
20#10622555—22no—
21C11×#342—22no—
22#10622165—22no—
23#10622165—22no—
24#10622164—22no—
25#10622164—22no—
26C25×C11C2311yescharacteristic
27C23×C4×C11—21no—
28C23×C4×C11—21no—
29C23×C4×C11C2×C412yes—
30C23×Dic11—21no—
31C23×Dic11—21no—
32C23×Dic11—21no—
33C23×Dic11D412yes—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4D412yes—
51C2×C11×C22⋊C4Q812yes—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—21no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11C2×C412yes—
70C2×C22⋊Dic11C2×C412yes—
71C2×C22⋊Dic11D412yes—
72C2×C22⋊Dic11D412yes—
73C2×C22⋊Dic11D412yes—
74C2×C22⋊Dic11Q812yes—
75C2×C22⋊Dic11Q812yes—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—24no—
78C11⋊#95—24no—
79C11⋊#95—24no—
80#11205—111nomaximal, Sylow
81C24×C11—82no—
82C24×C11C22×C411yescharacteristic
83C24×C11C2×D411yescharacteristic
84C24×C11C2×D411yescharacteristic
85C24×C11C2×D411yescharacteristic
86C24×C11C2×D411yescharacteristic
87C24×C11C2×D411yescharacteristic
88C24×C11C2×Q811yescharacteristic
89C24×C11C2×Q811yescharacteristic
90C24×C11C2×Q811yescharacteristic
91C24×C11#4111yescharacteristic
92C24×C11#4111yescharacteristic
93C24×C11#4111yescharacteristic
94C24×C11#4111yescharacteristic
95C24×C11#4111yescharacteristic
96C24×C11#4111yescharacteristic
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—82no—
107C22×C4×C11—82no—
108C22×C4×C11—82no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—82no—
121C22×Dic11—82no—
122C22×Dic11—82no—
123C22×Dic11—82no—
124C22×Dic11C22⋊C414yes—
125C11×C22⋊C4—22no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C22⋊Dic11—22no—
138C22⋊Dic11—22no—
139C22⋊Dic11—22no—
140C22⋊Dic11—22no—
141C22⋊Dic11—22no—
142C22⋊Dic11—22no—
143C22⋊Dic11—22no—
144C22⋊Dic11—22no—
145C22⋊Dic11—22no—
146C22⋊Dic11—22no—
147C22⋊Dic11—22no—
148C22⋊Dic11—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11C4⋊C414yescomplemented
153Dic11⋊C4—84no—
154Dic11⋊C4—84no—
155#2315—111no—
156#2315—111no—
157C2×#342—111no—
158C2×#342—111no—
159C2×#342—111no—
160C2×#342—111no—
161C2×#342D1111yescharacteristic
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—81no—
170C23×C11—81no—
171C23×C11—81no—
172C23×C11—81no—
173C23×C11—81no—
174C23×C11—81no—
175C23×C11—81no—
176C23×C11—81no—
177C23×C11C2×C22⋊C411yescharacteristic
178C23×C11C2×C4⋊C411yescharacteristic
179C23×C11#11711yescharacteristic
180C23×C11C4×D411yescharacteristic
181C23×C11C4×D411yescharacteristic
182C23×C11C4×Q811yescharacteristic
183C23×C11C4×Q811yescharacteristic
184C23×C11#12011yescharacteristic
185C23×C11#12111yescharacteristic
186C23×C11#12111yescharacteristic
187C23×C11#12111yescharacteristic
188C23×C11#12111yescharacteristic
189C23×C11#12111yescharacteristic
190C23×C11#12111yescharacteristic
191C23×C11C22⋊Q811yescharacteristic
192C23×C11C22⋊Q811yescharacteristic
193C23×C11C22⋊Q811yescharacteristic
194C23×C11C22⋊Q811yescharacteristic
195C23×C11C22⋊Q811yescharacteristic
196C23×C11C22⋊Q811yescharacteristic
197C23×C11C22⋊Q811yescharacteristic
198C23×C11C22⋊Q811yescharacteristic
199C23×C11#12311yescharacteristic
200C23×C11#12311yescharacteristic
201C23×C11#12311yescharacteristic
202C23×C11#12411yescharacteristic
203C23×C11#12511yescharacteristic
204C23×C11#12511yescharacteristic
205C23×C11#12511yescharacteristic
206C23×C11#12511yescharacteristic
207C23×C11#12611yescharacteristic
208C23×C11#12611yescharacteristic
209C23×C11C4⋊Q811yescharacteristic
210C23×C11C4⋊Q811yescharacteristic
211C23×C11C4⋊Q811yescharacteristic
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—82no—
218C2×C4×C11—82no—
219C2×C4×C11—82no—
220C2×C4×C11—82no—
221C2×C4×C11—82no—
222C2×C4×C11—82no—
223C2×C4×C11—82no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—44no—
227C2×Dic11—44no—
228C2×Dic11—44no—
229C2×Dic11—44no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—82no—
233C2×Dic11—82no—
234C2×Dic11—82no—
235C2×Dic11—82no—
236C2×Dic11—82no—
237C2×Dic11—82no—
238C2×Dic11—82no—
239C2×Dic11—82no—
240C22×C22⋊C4—111no—
241C22×C22⋊C4—111no—
242C22×C22⋊C4—111no—
243C22×C22⋊C4—111no—
244C22×C22⋊C4C2×D1111yescharacteristic
245C22×C22⋊C4C2×D1111yescharacteristic
246C22×C22⋊C4C2×D1111yescharacteristic
247#385—114no—
248#385—222no—
249#385—222no—
250#385—222no—
251#380—222no—
252#380—222no—
253#342—22no—
254#342—222no—
255#342—222no—
256#342—222no—
257#342—222no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11#38011yescharacteristic
294C22×C11#38611yescharacteristic
295C22×C11#38711yescharacteristic
296C22×C11#38711yescharacteristic
297C22×C11#38911yescharacteristic
298C22×C11#38911yescharacteristic
299C22×C11#39111yescharacteristic
300C22×C11#39411yescharacteristic
301C22×C11#39511yescharacteristic
302C22×C11#39611yescharacteristic
303C22×C11#39611yescharacteristic
304C22×C11#39811yescharacteristic
305C22×C11#39811yescharacteristic
306C22×C11#39811yescharacteristic
307C22×C11#40011yescharacteristic
308C4×C11—82no—
309C4×C11—82no—
310C4×C11—82no—
311Dic11—44no—
312Dic11—44no—
313Dic11—82no—
314Dic11—82no—
315C25C22×D1111yescharacteristic
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—112no—
319C23×C4—221no—
320C23×C4—221no—
321C23×C4—221no—
322C23×C4C4×D1112yes—
323C2×C4⋊C4—224no—
324C2×C4⋊C4—224no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—112no—
342C2×C22⋊C4—112no—
343C2×C22⋊C4—112no—
344C2×C22⋊C4—112no—
345C2×C22⋊C4—112no—
346C2×C22⋊C4—112no—
347C2×C22⋊C4—112no—
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—221no—
359C2×C22⋊C4—221no—
360C2×C22⋊C4—221no—
361C2×C22⋊C4—221no—
362C2×C22⋊C4—221no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4Dic2212yes—
366C2×C22⋊C4C22⋊D1112yes—
367#95—224no—
368#95—224no—
369C2×C11—21no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—21no—
374C2×C11—21no—
375C2×C11—21no—
376C2×C11—21no—
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11#144111yescharacteristic
384C2×C11#191312yes—
385C24—82no—
386C24C2×Dic2211yescharacteristic
387C24C2×C4×D1111yescharacteristic
388C24#433911yescharacteristic
389C24#433911yescharacteristic
390C24#433911yescharacteristic
391C24#433911yescharacteristic
392C24D4×D1111yescharacteristic
393C24D4×D1111yescharacteristic
394C24D4×D1111yescharacteristic
395C24D4×D1111yescharacteristic
396C24#434111yescharacteristic
397C24#434111yescharacteristic
398C24Q8×D1111yescharacteristic
399C24Q8×D1111yescharacteristic
400C24C2×C22⋊D1111yescharacteristic
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—82no—
411C22×C4—82no—
412C22×C4—82no—
413C22×C4—114no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—441no—
422C22×C4—441no—
423C22×C4—441no—
424C22×C4—441no—
425C22×C4—882no—
426C22×C4—882no—
427C22×C4—882no—
428C22×C4—882no—
429C4⋊C4—884no—
430C4⋊C4—884no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—114no—
444C22⋊C4—222no—
445C22⋊C4—222no—
446C22⋊C4—222no—
447C22⋊C4—222no—
448C22⋊C4—222no—
449C22⋊C4—222no—
450C22⋊C4—222no—
451C22⋊C4—222no—
452C22⋊C4—222no—
453C22⋊C4—222no—
454C22⋊C4—222no—
455C22⋊C4—441no—
456C22⋊C4—441no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C11#1120511yescharacteristic, complemented, Sylow
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—81no—
468C23—81no—
469C23—81no—
470C23—81no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23C4×Dic2211yescharacteristic
476C23#6692311yescharacteristic
477C23#6692511yescharacteristic
478C23#6692911yescharacteristic
479C23#6693111yescharacteristic
480C23#6693111yescharacteristic
481C23#6693211yescharacteristic
482C23C22⋊C4×D1111yescharacteristic
483C23(C22⋊D11)⋊C411yescharacteristic
484C23#6693611yescharacteristic
485C23#6693611yescharacteristic
486C23#6693711yescharacteristic
487C23#6693711yescharacteristic
488C23#6693711yescharacteristic
489C23#6693711yescharacteristic
490C23#6693811yescharacteristic
491C23#6694011yescharacteristic
492C23#6694111yescharacteristic
493C23#6694111yescharacteristic
494C23#6694211yescharacteristic
495C23#6694211yescharacteristic
496C23#6694211yescharacteristic
497C23C4⋊C4×D1111yescharacteristic
498C23#6694911yescharacteristic
499C23#6694911yescharacteristic
500C23#6694911yescharacteristic
501C23#6694911yescharacteristic
502C23#6694911yescharacteristic
503C23#6697711yescharacteristic
504C23C4×C22⋊D1111yescharacteristic
505C23#6698211yescharacteristic
506C23#6699011yescharacteristic
507C23#6699111yescharacteristic
508C23#6699211yescharacteristic
509C23#6699711yescharacteristic
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—444no—
525C2×C4—444no—
526C2×C4—444no—
527C2×C4—444no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—882no—
531C2×C4—882no—
532C2×C4—882no—
533C2×C4—882no—
534C2×C4—882no—
535C2×C4—882no—
536C2×C4—882no—
537C2×C4—882no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22#1062225911yescharacteristic
574C22#1062226011yescharacteristic
575C22#1062226511yescharacteristic
576C22#1062227011yescharacteristic
577C22#1062227011yescharacteristic
578C22#1062227111yescharacteristic
579C22#1062228011yescharacteristic
580C22#1062228911yescharacteristic
581C22#1062254611yescharacteristic
582C22#1062256111yescharacteristic
583C22#1062256911yescharacteristic
584C22#1062257211yescharacteristic
585C22#1062258511yescharacteristic
586C22#1062259211yescharacteristic
587C22#1062259311yescharacteristic
588C4—82no—
589C4—82no—
590C4—82no—
591C4—444no—
592C4—444no—
593C4—882no—
594C4—882no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2#1306686711yescharacteristic
610C2#1306915512yes—
subgroupG/H
centerC22#10622569
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC2×C11×#342C2
socleC22×C11#386
prime radical, cosocleC25×C11C23
hypercenterC2×#342D11
hypocenterC11#11205
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
16. #10622823C4semidirect
152. C22⋊Dic11C4⋊C4semidirect
459. C11#11205semidirect

Maximal subgroups

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

subgroupindex
#130712282
C2×#106221642
C2×#106221652
C2×C11×#3422
#1120511