Finite Group Databasebeta

← #14660697

Subgroups — #14660697

Order 2816.

1454 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66898C212yesmaximal
2C2×#10622825C211yesmaximal, characteristic, complemented
3C2×#10622164C212yesmaximal, complemented
4#13066839C211yesmaximal, characteristic, complemented
5C2×C11×#386C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C24×C4×C11C2211yescharacteristic
8C22×C11×C22⋊C4C412yescomplemented
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11C2212yes—
11C22×C22⋊Dic11C2212yes—
12C22×C4⋊Dic11—21no—
13C11×#386—21no—
14C11×#386—22no—
15C11×#386—21no—
16C2×C11×#95C412yescomplemented
17C2×#66898—24no—
18C2×#66898—24no—
19C2×#66898—24no—
20#10622825—24no—
21C2×C11⋊#95—21no—
22C2×C11⋊#95—22no—
23#10622164—24no—
24C25×C11C2×C411yescharacteristic
25C25×C11C2311yescharacteristic
26C22×D4×C11—22no—
27C22×D4×C11—22no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11D412yes—
35C22×D4×C11Q812yes—
36C23×C4×C11—22no—
37C23×C4×C11—22no—
38C23×C4×C11—44no—
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C412yes—
41C23×C4×C11C2×C412yes—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D412yes—
44C23×C4×C11D411yescharacteristic
45C23×Dic11—22no—
46C23×Dic11—22no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—44no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11D414yes—
65C2×C22⋊Dic11D414yes—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—44no—
68C11×#95—22no—
69C11×#95—22no—
70#66898—216no—
71C11⋊#95—24no—
72C11⋊#95—44no—
73#11043—111nomaximal, Sylow
74C24×C11—21no—
75C24×C11—21no—
76C24×C11—22no—
77C24×C11—22no—
78C24×C11—42no—
79C24×C11—42no—
80C24×C11—42no—
81C24×C11—42no—
82C24×C11C4⋊C412yescomplemented
83C24×C11C22×C411yescharacteristic
84C24×C11C2×D411yescharacteristic
85C24×C11C2×D411yescharacteristic
86C24×C11C2×D411yescharacteristic
87C24×C11C2×D412yes—
88C24×C11C2×D412yes—
89C24×C11C2×Q811yescharacteristic
90C24×C11#4111yescharacteristic
91C24×C11#4111yescharacteristic
92C24×C11#4112yes—
93C24×C11#4112yes—
94C2×D4×C11—24no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—41no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—41no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—41no—
110C2×D4×C11—42no—
111C2×D4×C11—41no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—24no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—24no—
122C22×C4×C11—21no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—48no—
131C22×C4×C11—48no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C22⋊C412yes—
135C22×C4×C11C22⋊C412yes—
136C22×C4×C11C4⋊C412yescomplemented
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—44no—
140C22×Dic11—44no—
141C22×Dic11—44no—
142C22×Dic11—44no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—42no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—44no—
152C22⋊Dic11—24no—
153C22⋊Dic11—24no—
154C22⋊Dic11—24no—
155C22⋊Dic11—24no—
156C22⋊Dic11—42no—
157C22⋊Dic11—42no—
158C22⋊Dic11—42no—
159C22⋊Dic11—42no—
160C4⋊Dic11—48no—
161C22×#99—112no—
162C2×#386D1111yescharacteristic
163C2×#380—111no—
164C2×#342—112no—
165C22⋊#95—111no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—24no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—44no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11—41no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—82no—
192C23×C11—82no—
193C23×C11—84no—
194C23×C11C2×C22⋊C411yescharacteristic
195C23×C11C2×C4⋊C411yescharacteristic
196C23×C11#11711yescharacteristic
197C23×C11C4×D412yes—
198C23×C11C4×D412yes—
199C23×C11#12012yes—
200C23×C11#12011yescharacteristic
201C23×C11#12112yes—
202C23×C11#12111yescharacteristic
203C23×C11#12111yescharacteristic
204C23×C11#12112yes—
205C23×C11#12112yes—
206C23×C11C22⋊Q812yes—
207C23×C11C22⋊Q812yes—
208C23×C11C22⋊Q811yescharacteristic
209C23×C11C22⋊Q811yescharacteristic
210C23×C11#12312yes—
211C23×C11#12312yes—
212C23×C11#12311yescharacteristic
213C23×C11#12412yes—
214C23×C11#12411yescharacteristic
215C23×C11#12612yes—
216C23×C11#12711yescharacteristic
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—44no—
220D4×C11—44no—
221D4×C11—42no—
222D4×C11—42no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—48no—
233C2×C4×C11—48no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—84no—
243C2×C4×C11#9914yescomplemented
244C2×Dic11—44no—
245C2×Dic11—44no—
246C2×Dic11—48no—
247C2×Dic11—44no—
248C2×Dic11—44no—
249C2×Dic11—84no—
250C2×Dic11—84no—
251C2×Dic11—82no—
252C2×Dic11—82no—
253C2×Dic11—84no—
254C23×D4C2×D1111yescharacteristic
255C24×C4C2×D1111yescharacteristic
256C22×C4⋊C4—221no—
257C22×C22⋊C4—112no—
258C22×C22⋊C4—112no—
259C22×C22⋊C4Dic1112yescomplemented
260C22×C22⋊C4C2×D1111yescharacteristic
261C2×#99—224no—
262C2×#99—224no—
263C2×#99—224no—
264#386—21no—
265#386—22no—
266#386—21no—
267#380—224no—
268C2×#95—221no—
269C2×#95—222no—
270C2×#95Dic1112yescomplemented
271#342—224no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—21no—
284C22×C11—22no—
285C22×C11—21no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—42no—
300C22×C11—84no—
301C22×C11—84no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—82no—
305C22×C11#38011yescharacteristic
306C22×C11#38512yes—
307C22×C11#38611yescharacteristic
308C22×C11#38812yes—
309C22×C11#39011yescharacteristic
310C22×C11#39211yescharacteristic
311C22×C11#39311yescharacteristic
312C22×C11#39412yes—
313C22×C11#39612yes—
314C22×C11#39711yescharacteristic
315C22×C11#39911yescharacteristic
316C22×C11C2×#9912yes—
317C22×C11#41012yes—
318C4×C11—24no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11—82no—
322Dic11—84no—
323Dic11—84no—
324C25C2×Dic1111yescharacteristic
325C25C22×D1111yescharacteristic
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4Dic2212yes—
335C22×D4D4412yes—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—44no—
339C23×C4—222no—
340C23×C4—222no—
341C23×C4C2×Dic1111yescharacteristic
342C23×C4C2×Dic1112yes—
343C23×C4C2×Dic1112yes—
344C23×C4C22⋊D1111yescharacteristic
345C23×C4C22⋊D1112yes—
346C23×C4C22⋊D1111yescharacteristic
347C2×C4⋊C4—224no—
348C2×C4⋊C4—444no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—114no—
357C2×C22⋊C4—114no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368#99—2216no—
369#95—22no—
370#95—22no—
371#95—224no—
372#95—444no—
373C2×C11—21no—
374C2×C11—22no—
375C2×C11—22no—
376C2×C11—22no—
377C2×C11—21no—
378C2×C11—22no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11—82no—
382C2×C11#143911yescharacteristic
383C2×C11#179912yes—
384C2×C11#189811yescharacteristic
385C2×C11#189911yescharacteristic
386C2×C11#196412yes—
387C24—21no—
388C24—21no—
389C24—22no—
390C24—22no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24C4⋊Dic1112yescomplemented
396C24C2×Dic2211yescharacteristic
397C24C2×D4411yescharacteristic
398C24#433911yescharacteristic
399C24#433911yescharacteristic
400C24D4×D1112yes—
401C24D4×D1112yes—
402C24#434112yes—
403C24#434112yes—
404C24C22×Dic1111yescharacteristic
405C24C2×C22⋊D1111yescharacteristic
406C24C2×C22⋊D1111yescharacteristic
407C2×D4—24no—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—41no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—24no—
435C22×C4—21no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—48no—
444C22×C4—48no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—444no—
450C22×C4—444no—
451C22×C4—444no—
452C22×C4—444no—
453C22×C4—442no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4C4⋊Dic1112yescomplemented
458C22×C4C22⋊Dic1112yes—
459C22×C4C22⋊Dic1112yes—
460C4⋊C4—448no—
461C22⋊C4—44no—
462C22⋊C4—41no—
463C22⋊C4—42no—
464C22⋊C4—41no—
465C22⋊C4—44no—
466C22⋊C4—224no—
467C22⋊C4—224no—
468C22⋊C4—224no—
469C22⋊C4—224no—
470C22⋊C4—442no—
471C22⋊C4—442no—
472C22⋊C4—442no—
473C22⋊C4—442no—
474C11#1104311yescharacteristic, complemented, Sylow
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—42no—
496C23—42no—
497C23—41no—
498C23—41no—
499C23—42no—
500C23—82no—
501C23—82no—
502C23—84no—
503C23#6693112yes—
504C23#6693112yes—
505C23#6693212yes—
506C23#6693512yes—
507C23#6693612yes—
508C23#6693712yes—
509C23#6693812yes—
510C23#6693912yes—
511C23#6697711yescharacteristic
512C23#6697711yescharacteristic
513C23C2×C4⋊Dic1111yescharacteristic
514C23#6697911yescharacteristic
515C23#6698311yescharacteristic
516C23#6698311yescharacteristic
517C23D4×Dic1112yes—
518C23D4×Dic1112yes—
519C23#6698811yescharacteristic
520C23#6698911yescharacteristic
521C23#6699011yescharacteristic
522C23#6699112yes—
523C23#6699212yes—
524C23#6699311yescharacteristic
525C23C2×C22⋊Dic1111yescharacteristic
526D4—42no—
527D4—44no—
528D4—42no—
529D4—42no—
530D4—42no—
531D4—44no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—48no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—84no—
552C2×C4—444no—
553C2×C4—444no—
554C2×C4—448no—
555C2×C4—444no—
556C2×C4—444no—
557C2×C4—882no—
558C2×C4—882no—
559C2×C4—884no—
560C2×C4—884no—
561C2×C4—884no—
562C2×C4#6689814yescomplemented
563C22—21no—
564C22—21no—
565C22—22no—
566C22—22no—
567C22—21no—
568C22—22no—
569C22—22no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—24no—
578C22—24no—
579C22—22no—
580C22—22no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—42no—
591C22—84no—
592C22—84no—
593C22—81no—
594C22—81no—
595C22—82no—
596C22#1062256011yescharacteristic
597C22#1062256112yes—
598C22#1062256211yescharacteristic
599C22#1062256312yes—
600C22#1062256412yes—
601C22#1062256611yescharacteristic
602C22#1062257311yescharacteristic
603C22#1062257412yes—
604C22#1062282511yescharacteristic
605C22C2×#6689812yes—
606C22#1062283311yescharacteristic
607C22#1062283411yescharacteristic
608C22#1062285312yes—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—82no—
613C4—884no—
614C4—884no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—22no—
619C2—21no—
620C2—22no—
621C2—21no—
622C2—21no—
623C2—82no—
624C2#1306686111yescharacteristic
625C2#1306860412yes—
626C2#1306907011yescharacteristic
627C2#1306907511yescharacteristic
628C2#1306945312yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC2×C11×#386C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D4×C11C22
cosocleC25×C11C23
hypercenterC2×#386D11
hypocenterC11#11043
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#10622825C2semidirect
3. C2×#10622164C2semidirect
4. #13066839C2semidirect
8. C22×C11×C22⋊C4C4semidirect
16. C2×C11×#95C4semidirect
82. C24×C11C4⋊C4semidirect
136. C22×C4×C11C4⋊C4semidirect
243. C2×C4×C11#99semidirect
259. C22×C22⋊C4Dic11semidirect
270. C2×#95Dic11semidirect
395. C24C4⋊Dic11semidirect
457. C22×C4C4⋊Dic11semidirect
474. C11#11043semidirect
562. C2×C4#66898semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
C2×#106228252
C2×#106221642
#130668392
C2×C11×#3862
#1104311