Finite Group Databasebeta

← #14660698

Subgroups — #14660698

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×#66870C212yesmaximal
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622825C211yesmaximal, characteristic, complemented
4C2×#10622165C212yesmaximal, complemented
5C11×C22⋊#95C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C23×C22⋊D11C2211yescharacteristic
8C22×C11×C22⋊C4C2212yes—
9C22×C22⋊Dic11C2211yescharacteristic
10C22×C22⋊Dic11C2212yes—
11C22×(C2×D11)⋊C4C412yescomplemented
12C22×C4⋊Dic11—21no—
13C2×C11×#95—22no—
14#10622826—21no—
15#10622826—21no—
16#10622826—22no—
17#10622825—24no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C412yescomplemented
20C2×#66870—24no—
21C2×#66870—24no—
22C2×#66870—24no—
23#10622165—24no—
24C25×C11C2311yescharacteristic
25C24×D11C2×C411yescharacteristic
26C23×C4×C11—22no—
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—44no—
30C23×C4×C11C2×C412yes—
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D412yes—
34C22×C22⋊D11—22no—
35C22×C22⋊D11—22no—
36C22×C22⋊D11—21no—
37C22×C22⋊D11—21no—
38C22×C22⋊D11—22no—
39C22×C22⋊D11—21no—
40C22×C22⋊D11—22no—
41C22×C22⋊D11—21no—
42C22×C22⋊D11D412yes—
43C22×C22⋊D11Q812yes—
44C23×Dic11—22no—
45C23×Dic11C2×C411yescharacteristic
46C23×Dic11C2×C412yes—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4D414yes—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11D414yes—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—44no—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—44no—
68C11×#95—44no—
69C11⋊#95—24no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72#66870—216no—
73#11043—111nomaximal, Sylow
74C24×C11—42no—
75C24×C11—42no—
76C24×C11C22×C411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C24×C11C2×D411yescharacteristic
79C24×C11C2×D411yescharacteristic
80C24×C11C2×D412yes—
81C24×C11C2×D412yes—
82C24×C11C2×Q811yescharacteristic
83C24×C11#4111yescharacteristic
84C24×C11#4111yescharacteristic
85C24×C11#4112yes—
86C24×C11#4112yes—
87C23×D11—21no—
88C23×D11—21no—
89C23×D11—22no—
90C23×D11—22no—
91C23×D11—42no—
92C23×D11—42no—
93C23×D11C4⋊C412yescomplemented
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—21no—
99C22×C4×C11—24no—
100C22×C4×C11—21no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—48no—
108C22×C4×C11—48no—
109C22×C4×C11—44no—
110C22×C4×C11—44no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C22⋊C412yes—
114C22×C4×C11C22⋊C412yes—
115C2×C22⋊D11—24no—
116C2×C22⋊D11—22no—
117C2×C22⋊D11—22no—
118C2×C22⋊D11—22no—
119C2×C22⋊D11—22no—
120C2×C22⋊D11—24no—
121C2×C22⋊D11—24no—
122C2×C22⋊D11—24no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—42no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—42no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—42no—
129C2×C22⋊D11—42no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—42no—
132C2×C22⋊D11—41no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—44no—
141C22×Dic11—44no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11C4⋊C412yescomplemented
147C11×C22⋊C4—24no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—42no—
150C11×C22⋊C4—42no—
151C22⋊Dic11—24no—
152C22⋊Dic11—24no—
153C22⋊Dic11—42no—
154C22⋊Dic11—42no—
155C22⋊Dic11—42no—
156C22⋊Dic11—41no—
157C22⋊Dic11—41no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—44no—
160C4⋊Dic11—48no—
161C22×#99—112no—
162C2×#386—111no—
163C2×#380—111no—
164C2×#342—112no—
165C22⋊#95D1111yescharacteristic, complemented
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—44no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—44no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11C2×C22⋊C411yescharacteristic
183C23×C11C2×C4⋊C411yescharacteristic
184C23×C11#11711yescharacteristic
185C23×C11C4×D412yes—
186C23×C11C4×D412yes—
187C23×C11#12011yescharacteristic
188C23×C11#12012yes—
189C23×C11#12111yescharacteristic
190C23×C11#12112yes—
191C23×C11#12112yes—
192C23×C11#12111yescharacteristic
193C23×C11#12112yes—
194C23×C11C22⋊Q812yes—
195C23×C11C22⋊Q811yescharacteristic
196C23×C11C22⋊Q812yes—
197C23×C11C22⋊Q811yescharacteristic
198C23×C11#12312yes—
199C23×C11#12311yescharacteristic
200C23×C11#12312yes—
201C23×C11#12411yescharacteristic
202C23×C11#12412yes—
203C23×C11#12612yes—
204C23×C11#12711yescharacteristic
205C22×D11—22no—
206C22×D11—24no—
207C22×D11—44no—
208C22×D11—41no—
209C22×D11—42no—
210C22×D11—41no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—44no—
214C22×D11—82no—
215C22×D11—82no—
216C22×D11—84no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—48no—
225C2×C4×C11—48no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—48no—
229C2×C4×C11—44no—
230C2×C4×C11—84no—
231C2×C4×C11—82no—
232C2×C4×C11—82no—
233C2×C4×C11#9914yescomplemented
234C22⋊D11—42no—
235C22⋊D11—42no—
236C22⋊D11—44no—
237C22⋊D11—44no—
238C22⋊D11—42no—
239C22⋊D11—42no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—41no—
245C2×Dic11—44no—
246C2×Dic11—44no—
247C2×Dic11—42no—
248C2×Dic11—44no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—84no—
252C2×Dic11—84no—
253C2×Dic11—84no—
254C23×D4—111no—
255C24×C4C2×D1111yescharacteristic
256C22×C4⋊C4—221no—
257C22×C22⋊C4—112no—
258C22×C22⋊C4—111no—
259C22×C22⋊C4—112no—
260C22×C22⋊C4C2×D1112yes—
261C2×#99—224no—
262C2×#99—224no—
263C2×#99—224no—
264#386—221no—
265#386—221no—
266#386—222no—
267#380—224no—
268C2×#95—22no—
269C2×#95—112no—
270C2×#95—221no—
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—22no—
284C22×C11—21no—
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#38011yescharacteristic
299C22×C11#38512yes—
300C22×C11#38611yescharacteristic
301C22×C11#38812yes—
302C22×C11#39011yescharacteristic
303C22×C11#39211yescharacteristic
304C22×C11#39311yescharacteristic
305C22×C11#39412yes—
306C22×C11#39612yes—
307C22×C11#39711yescharacteristic
308C22×C11#39911yescharacteristic
309C22×C11C2×#9912yes—
310C22×C11#41012yes—
311C2×D11—44no—
312C2×D11—42no—
313C2×D11—84no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—82no—
317C2×D11—84no—
318C4×C11—24no—
319C4×C11—42no—
320C4×C11—84no—
321Dic11—42no—
322Dic11—84no—
323Dic11—82no—
324C25—111no—
325C25C22×D1111yescharacteristic
326C22×D4—112no—
327C22×D4—112no—
328C22×D4—221no—
329C22×D4—222no—
330C22×D4—222no—
331C22×D4—222no—
332C22×D4—222no—
333C22×D4—221no—
334C22×D4—221no—
335C22×D4—221no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—44no—
340C23×C4—111no—
341C23×C4—112no—
342C23×C4—222no—
343C23×C4C4×D1112yes—
344C23×C4D4411yescharacteristic
345C23×C4D4411yescharacteristic
346C23×C4C22⋊D1112yes—
347C2×C4⋊C4—224no—
348C2×C4⋊C4—444no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—114no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—221no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—444no—
367C2×C22⋊C4D4414yes—
368#99—2216no—
369#95—44no—
370#95—224no—
371#95—222no—
372#95—222no—
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#143911yescharacteristic
382C2×C11#179912yes—
383C2×C11#189811yescharacteristic
384C2×C11#189911yescharacteristic
385C2×C11#196412yes—
386D11—82no—
387C24—42no—
388C24—42no—
389C24—112no—
390C24—221no—
391C24—221no—
392C24—222no—
393C24—222no—
394C24—442no—
395C24—442no—
396C24C2×C4×D1111yescharacteristic
397C24C2×D4411yescharacteristic
398C24C2×D4412yes—
399C24#433912yes—
400C24D4×D1112yes—
401C24D4×D1111yescharacteristic
402C24#434112yes—
403C24#434111yescharacteristic
404C24Q8×D1111yescharacteristic
405C24#434311yescharacteristic
406C24C2×C22⋊D1111yescharacteristic
407C2×D4—224no—
408C2×D4—224no—
409C2×D4—222no—
410C2×D4—224no—
411C2×D4—224no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—222no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—442no—
419C2×D4—442no—
420C2×D4—441no—
421C2×D4—442no—
422C2×D4—442no—
423C2×D4—442no—
424C2×D4—442no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—48no—
439C22×C4—48no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—112no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—224no—
450C22×C4—222no—
451C22×C4—224no—
452C22×C4—444no—
453C22×C4—444no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4(C2×D11)⋊C412yes—
459C22×C4(C2×D11)⋊C412yes—
460C4⋊C4—448no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—42no—
464C22⋊C4—42no—
465C22⋊C4—224no—
466C22⋊C4—224no—
467C22⋊C4—444no—
468C22⋊C4—441no—
469C22⋊C4—441no—
470C22⋊C4—442no—
471C22⋊C4—442no—
472C22⋊C4—442no—
473C22⋊C4—444no—
474C11#1104311yescharacteristic, complemented, Sylow
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—42no—
482C23—42no—
483C23—44no—
484C23—44no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—222no—
492C23—224no—
493C23—444no—
494C23—444no—
495C23—442no—
496C23—441no—
497C23—442no—
498C23—441no—
499C23—442no—
500C23—882no—
501C23—882no—
502C23—884no—
503C23C4×D4412yes—
504C23#6692711yescharacteristic
505C23#6692811yescharacteristic
506C23(C22⋊D11)⋊C412yes—
507C23#6693511yescharacteristic
508C23#6693512yes—
509C23#6693612yes—
510C23#6693812yes—
511C23#6693911yescharacteristic
512C23#6693912yes—
513C23C4⋊C4×D1111yescharacteristic
514C23#6694511yescharacteristic
515C23#6694811yescharacteristic
516C23#6694812yes—
517C23#6694912yes—
518C23#6695011yescharacteristic
519C23#6695012yes—
520C23#6695112yes—
521C23C2×(C2×D11)⋊C411yescharacteristic
522C23#6698312yes—
523C23#6699111yescharacteristic
524C23#6699212yes—
525C23#6699911yescharacteristic
526D4—442no—
527D4—442no—
528D4—442no—
529D4—442no—
530D4—444no—
531D4—444no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—48no—
540C2×C4—48no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—48no—
544C2×C4—44no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—84no—
548C2×C4—224no—
549C2×C4—222no—
550C2×C4—442no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—444no—
554C2×C4—444no—
555C2×C4—444no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—884no—
560C2×C4—884no—
561C2×C4—884no—
562C2×C4#6687014yescomplemented
563C22—21no—
564C22—21no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—21no—
569C22—22no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—24no—
578C22—22no—
579C22—24no—
580C22—22no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—444no—
590C22—442no—
591C22—884no—
592C22—884no—
593C22—881no—
594C22—881no—
595C22—882no—
596C22#1062228112yes—
597C22#1062228312yes—
598C22#1062228411yescharacteristic
599C22#1062228611yescharacteristic
600C22#1062228711yescharacteristic
601C22#1062229011yescharacteristic
602C22#1062255211yescharacteristic
603C22C2×#6687012yes—
604C22#1062257111yescharacteristic
605C22#1062257412yes—
606C22#1062260011yescharacteristic
607C22#1062260712yes—
608C22#1062261912yes—
609C4—24no—
610C4—42no—
611C4—84no—
612C4—442no—
613C4—884no—
614C4—882no—
615C2—22no—
616C2—21no—
617C2—22no—
618C2—22no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—22no—
623C2—882no—
624C2#1306686211yescharacteristic
625C2#1306860112yes—
626C2#1306906711yescharacteristic
627C2#1306907211yescharacteristic
628C2#1306945212yes—
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×C22⋊#95C2
socleC23×C11C2×C22⋊C4
prime radicalC23×C22⋊D11C22
cosocleC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#11043
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622825C2semidirect
4. C2×#10622165C2semidirect
5. C11×C22⋊#95C2semidirect
11. C22×(C2×D11)⋊C4C4semidirect
19. C2×C11⋊#95C4semidirect
93. C23×D11C4⋊C4semidirect
146. C22×Dic11C4⋊C4semidirect
165. C22⋊#95D11semidirect
233. C2×C4×C11#99semidirect
474. C11#11043semidirect
562. C2×C4#66870semidirect

Maximal subgroups

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

subgroupindex
C22×#668702
C2×#106228262
C2×#106228252
C2×#106221652
C11×C22⋊#952
#1104311