Finite Group Databasebeta

← #14660751

Subgroups — #14660751

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622744C211yesmaximal, characteristic
2C2×#10622614C211yesmaximal, characteristic
3#13071232C211yesmaximal, characteristic, complemented
4C2×#10622552C211yesmaximal, characteristic
5C2×#10622192C211yesmaximal, characteristic, complemented
6C2×#10622161C211yesmaximal, characteristic, complemented
7C2×C11×#339C211yesmaximal, characteristic, complemented
8C23×D44C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×(C2×D11)⋊C4—22no—
13C2×#66979C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16#10622744—22no—
17#10622744—22no—
18C2×#66885—22no—
19#10622614—22no—
20#10622614—22no—
21#10622586—22no—
22C2×#66873—22no—
23#10622555—22no—
24#10622552—22no—
25#10622552C414yescomplemented
26#10622541—22no—
27C11×#339—22no—
28#10622192—22no—
29#10622161—22no—
30C24×D11—21no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C23×Dic11D412yes—
34C22×D44—21no—
35C22×D44—21no—
36C22×D44—21no—
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44C2×C412yes—
46C22×D44D412yes—
47C22×D44Q812yes—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16D412yes—
54C22×C8×C11—21no—
55C11×#117—21no—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C42×C11—21no—
63C2×C42×C11—21no—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2×C412yes—
68C2×C22⋊Dic11—21no—
69C2×(C2×D11)⋊C4—28no—
70C2×(C2×D11)⋊C4—48no—
71#66979—21no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2×C412yes—
80C2×C4⋊Dic11D412yes—
81C2×C4⋊Dic11D412yes—
82C2×Dic11⋊C4—24no—
83C2×C4×Dic11—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318D412yes—
90C22×C11⋊C8—21no—
91C11⋊#95—24no—
92#66885—28no—
93#66873—28no—
94#11054—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—44no—
100C23×D11—44no—
101C23×D11—41no—
102C23×D11—41no—
103C23×D11—41no—
104C23×D11—41no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×Q811yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—44no—
129C22×Dic11C22⋊C414yes—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—41no—
146C2×D44—41no—
147C2×D44—41no—
148C2×D44—41no—
149C2×D44—41no—
150C2×D44—41no—
151C2×D44—41no—
152C2×D44—41no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—41no—
157C2×D44C4⋊C414yescomplemented
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—41no—
161C11×M16—41no—
162C2×C8×C11—22no—
163C2×C8×C11—41no—
164C2×C8×C11—41no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—41no—
172C42×C11—41no—
173C42×C11—41no—
174C42×C11—41no—
175C22⋊Dic11—41no—
176C22⋊Dic11—41no—
177(C2×D11)⋊C4—416no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184Dic11⋊C4—84no—
185C4×Dic11—41no—
186C4×Dic11—41no—
187#4318—22no—
188#4318—22no—
189#4318—41no—
190#4318—41no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—41no—
193C2×C11⋊C8—41no—
194C2×#418—111no—
195C2×#418—111no—
196#2316—111no—
197C2×#390—111no—
198C2×#343—111no—
199C2×#339—111no—
200C2×#339D1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11—22no—
203C23×C11C2×C22⋊C411yescharacteristic
204C23×C11#12011yescharacteristic
205C23×C11#12111yescharacteristic
206C23×C11C22⋊Q811yescharacteristic
207C23×C11#12311yescharacteristic
208C23×C11#12411yescharacteristic
209C23×C11#12711yescharacteristic
210C22×D11—24no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—48no—
214C22×D11—48no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—82no—
222C22×D11—82no—
223C22×D11—84no—
224C22×D11—84no—
225C22×D11—82no—
226C22×D11—82no—
227C2×C4×C11—24no—
228C2×C4×C11—42no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11C2×C4⋊C411yescharacteristic
236C2×C4×C11#11711yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11C22⋊Q811yescharacteristic
251C2×C4×C11C22⋊Q811yescharacteristic
252C2×C4×C11C22⋊Q811yescharacteristic
253C2×C4×C11C22⋊Q811yescharacteristic
254C2×C4×C11C22⋊Q811yescharacteristic
255C2×C4×C11#12311yescharacteristic
256C2×C4×C11#12311yescharacteristic
257C2×C4×C11#12311yescharacteristic
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12411yescharacteristic
260C2×C4×C11#12411yescharacteristic
261C2×C4×C11#12611yescharacteristic
262C2×C4×C11#12611yescharacteristic
263C2×Dic11—24no—
264C2×Dic11—44no—
265C2×Dic11—44no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—82no—
270D44—24no—
271D44—24no—
272D44—42no—
273D44—42no—
274D44—42no—
275D44—42no—
276D44—42no—
277D44—42no—
278C8×C11—42no—
279C11⋊C8—42no—
280C23×D4—111no—
281C22×M16—111no—
282C22×M16C2×D1111yescharacteristic
283C2×#117—111no—
284C2×#117C2×D1111yescharacteristic
285C22×C4⋊C4—111no—
286C22×C22⋊C4—222no—
287C22×C42C2×D1111yescharacteristic
288#418—222no—
289#418—222no—
290#418—222no—
291#418—222no—
292C2×#102—222no—
293C2×#102—222no—
294#390—114no—
295#390—222no—
296#389—222no—
297#389—222no—
298#380—222no—
299#343—222no—
300#339—22no—
301#339—222no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11#38011yescharacteristic
311C22×C11#38611yescharacteristic
312C22×C11#39011yescharacteristic
313C22×C11#39211yescharacteristic
314C22×C11#39311yescharacteristic
315C22×C11#39711yescharacteristic
316C22×C11#39911yescharacteristic
317C22×C11#45312yes—
318C22×C11#45412yes—
319C2×D11—48no—
320C2×D11—44no—
321C2×D11—84no—
322C2×D11—84no—
323C2×D11—84no—
324C2×D11—82no—
325C2×D11—82no—
326C2×D11—84no—
327C2×D11—84no—
328C4×C11—44no—
329C4×C11—82no—
330C4×C11#38511yescharacteristic
331C4×C11#38511yescharacteristic
332C4×C11#38811yescharacteristic
333C4×C11#38811yescharacteristic
334C4×C11#39411yescharacteristic
335C4×C11#39411yescharacteristic
336C4×C11#39611yescharacteristic
337C4×C11#39611yescharacteristic
338Dic11—44no—
339Dic11—82no—
340C25—221no—
341C22×D4—112no—
342C22×D4—112no—
343C22×D4—112no—
344C22×D4—221no—
345C22×D4—221no—
346C22×D4—221no—
347C22×D4—221no—
348C22×D4—221no—
349C22×D4—221no—
350C22×D4—221no—
351C22×D4—221no—
352C22×D4—221no—
353C22×D4—221no—
354C22×D4—221no—
355C23×C4—21no—
356C23×C4—112no—
357C23×C4C22×D1111yescharacteristic
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—112no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16C22⋊D1112yes—
370C22×C8—21no—
371C22×C8—221no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—221no—
377#117—221no—
378#117—221no—
379#117—221no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4D4412yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—448no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—221no—
400C2×C42C4×D1112yes—
401#102—228no—
402#102—228no—
403#95—224no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11#143911yescharacteristic
409C2×C11#188711yescharacteristic
410C2×C11#188811yescharacteristic
411C2×C11#200612yes—
412C2×C11#202712yes—
413D11—84no—
414C24—222no—
415C24—222no—
416C24—222no—
417C24—444no—
418C24—444no—
419C24—441no—
420C24—441no—
421C24—441no—
422C24—441no—
423C24D4×D1111yescharacteristic
424C2×D4—114no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—441no—
441C2×D4—441no—
442C2×D4—441no—
443C2×D4—441no—
444C2×D4—441no—
445C2×D4—441no—
446C2×D4—441no—
447C2×D4—441no—
448C2×D4—441no—
449C2×D4—441no—
450C2×D4—441no—
451C2×D4—441no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—42no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—114no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—444no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4C2×D4411yescharacteristic
465C22×C4#433911yescharacteristic
466C22×C4#433911yescharacteristic
467C22×C4#433911yescharacteristic
468C22×C4#433911yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4D4×D1111yescharacteristic
471C22×C4D4×D1111yescharacteristic
472C22×C4D4×D1111yescharacteristic
473C22×C4#434111yescharacteristic
474C22×C4Q8×D1111yescharacteristic
475C22×C4#434311yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477M16—22no—
478M16—22no—
479M16—41no—
480M16—41no—
481M16—222no—
482M16—222no—
483M16—441no—
484M16—441no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—222no—
489C2×C8—441no—
490C2×C8—441no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—222no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—884no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—4416no—
503C22⋊C4—441no—
504C22⋊C4—441no—
505C42—22no—
506C42—22no—
507C42—41no—
508C42—41no—
509C42—41no—
510C42—41no—
511C42—441no—
512C42—441no—
513C11#1105411yescharacteristic, complemented, Sylow
514C23—22no—
515C23—22no—
516C23—224no—
517C23—444no—
518C23—448no—
519C23—448no—
520C23—444no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—884no—
528C23—884no—
529C23—882no—
530C23—882no—
531C23—882no—
532C23—882no—
533C23C22⋊C4×D1111yescharacteristic
534C23#6693511yescharacteristic
535C23#6693711yescharacteristic
536C23#6693811yescharacteristic
537C23#6694711yescharacteristic
538C23#6694911yescharacteristic
539C23#6699311yescharacteristic
540D4—224no—
541D4—224no—
542D4—442no—
543D4—442no—
544D4—442no—
545D4—442no—
546D4—442no—
547D4—442no—
548C2×C4—24no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—224no—
557C2×C4—444no—
558C2×C4—444no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—882no—
563C2×C4#6692511yescharacteristic
564C2×C4C4×D4411yescharacteristic
565C2×C4#6692811yescharacteristic
566C2×C4#6692911yescharacteristic
567C2×C4(C22⋊D11)⋊C411yescharacteristic
568C2×C4#6693511yescharacteristic
569C2×C4#6693611yescharacteristic
570C2×C4#6693711yescharacteristic
571C2×C4#6693711yescharacteristic
572C2×C4#6693711yescharacteristic
573C2×C4#6693711yescharacteristic
574C2×C4#6693811yescharacteristic
575C2×C4C4⋊C4×D1111yescharacteristic
576C2×C4#6694611yescharacteristic
577C2×C4#6694711yescharacteristic
578C2×C4#6694711yescharacteristic
579C2×C4#6694811yescharacteristic
580C2×C4#6694911yescharacteristic
581C2×C4#6694911yescharacteristic
582C2×C4#6694911yescharacteristic
583C2×C4#6695011yescharacteristic
584C2×C4#6695111yescharacteristic
585C2×C4C4×C22⋊D1111yescharacteristic
586C2×C4#6698211yescharacteristic
587C2×C4#6698311yescharacteristic
588C2×C4#6699011yescharacteristic
589C2×C4#6699211yescharacteristic
590C2×C4#6699911yescharacteristic
591C8—42no—
592C8—442no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—448no—
602C22—444no—
603C22—884no—
604C22—884no—
605C22—884no—
606C22—884no—
607C22—884no—
608C22—882no—
609C22—882no—
610C22#1062227811yescharacteristic
611C22#1062228011yescharacteristic
612C22#1062228611yescharacteristic
613C22#1062228811yescharacteristic
614C22#1062243512yes—
615C22#1062244012yes—
616C22#1062257011yescharacteristic
617C22#1062257311yescharacteristic
618C22#1062260511yescharacteristic
619C4—44no—
620C4—82no—
621C4—444no—
622C4—882no—
623C4#1062228111yescharacteristic
624C4#1062228211yescharacteristic
625C4#1062228511yescharacteristic
626C4#1062228911yescharacteristic
627C4#1062255311yescharacteristic
628C4#1062257211yescharacteristic
629C4#1062260211yescharacteristic
630C4#1062260711yescharacteristic
631C2—21no—
632C2—21no—
633C2—21no—
634C2—21no—
635C2—884no—
636C2#1306686011yescharacteristic
637C2#1306901311yescharacteristic
638C2#1306901811yescharacteristic
639C2#1306965912yes—
640C2#1306977112yes—
subgroupG/H
centerC23#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#339C2
socleC23×C11#120
prime radicalC23×D44C22
cosocleC23×C4×C11C23
hypercenterC2×#339D11
hypocenterC11#11054
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
3. #13071232C2semidirect
5. C2×#10622192C2semidirect
6. C2×#10622161C2semidirect
7. C2×C11×#339C2semidirect
25. #10622552C4semidirect
157. C2×D44C4⋊C4semidirect
200. C2×#339D11semidirect
513. C11#11054semidirect

Maximal subgroups

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

subgroupindex
C2×#106227442
C2×#106226142
#130712322
C2×#106225522
C2×#106221922
C2×#106221612
C2×C11×#3392
#1105411