Finite Group Databasebeta

← #25004276

Subgroups — #25004276

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582917C211yesmaximal, characteristic
2C22×#13063251C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic
4#19134321C211yesmaximal, characteristic, complemented
5C2×#14582658C211yesmaximal, characteristic, complemented
6#19134288C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×C4×Dic43C2211yescharacteristic
12#14582917—22no—
13#14582917—22no—
14C2×#13063253—22no—
15C2×#13063251—22no—
16C2×#13063251—22no—
17C2×#13063251—22no—
18#14582881—22no—
19#14582881—22no—
20C2×#13063243C412yescomplemented
21C2×#13063241C412yescomplemented
22#14582663—22no—
23#14582658—22no—
24#14582653—22no—
25C22×M16×C43C2211yescharacteristic
26C22×M16×C43C2211yescharacteristic
27C2×#117×C43C2211yescharacteristic
28C43×#344—22no—
29C2×#10621898—21no—
30C2×#10621898—21no—
31C2×#10621898—21no—
32C2×#10621898—21no—
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898D412yes—
40C2×#10621898D412yes—
41C22×Dic86C2×C411yescharacteristic
42C22×D172C2×C411yescharacteristic
43C22×C22⋊D43—21no—
44C23×Dic43—21no—
45C22×C4×D43—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877C2×C412yes—
57C2×#10621877D412yes—
58C22×C43⋊C8—21no—
59C22×C43⋊C8—21no—
60C2×C4×Dic43—21no—
61C2×C4×Dic43—21no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43D412yes—
66#13063253—28no—
67#13063251—28no—
68#13063243—24no—
69#13063241—24no—
70C23×C4×C43C2311yescharacteristic
71C2×M16×C43—21no—
72C2×M16×C43—21no—
73C2×M16×C43—21no—
74C2×M16×C43—21no—
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43C2×C412yes—
82C2×M16×C43D412yes—
83C22×C8×C43—21no—
84C22×C8×C43—21no—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43—21no—
88#117×C43D412yes—
89C2×C4⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C42×C43—21no—
92C24×C43#4111yescharacteristic
93C23×D43—21no—
94C22×C4×C43—41no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C2×C22⋊D43—22no—
110C2×C22⋊D43—22no—
111C2×C22⋊D43—41no—
112C2×C22⋊D43—41no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C22×Dic43—21no—
116C22×Dic43—22no—
117C22×Dic43—44no—
118C22×Dic43—41no—
119C22×Dic43—41no—
120#10621898—22no—
121#10621898—22no—
122#10621898—22no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—41no—
129#10621898—41no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172C22⋊C412yes—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43—41no—
147C2×C4×D43—41no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86C22⋊C412yes—
154M16×C43—22no—
155M16×C43—22no—
156M16×C43—22no—
157M16×C43—22no—
158M16×C43—41no—
159M16×C43—41no—
160M16×C43—41no—
161M16×C43—41no—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43—41no—
165C2×C8×C43—41no—
166C2×C8×C43—41no—
167C2×C8×C43—41no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—41no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—41no—
172C42×C43—22no—
173C42×C43—41no—
174C4×Dic43—22no—
175C4×Dic43—22no—
176C4×Dic43—41no—
177C4×Dic43—41no—
178#10621877—22no—
179#10621877—22no—
180#10621877—22no—
181#10621877—22no—
182#10621877—41no—
183#10621877—41no—
184#10621877—41no—
185#10621877—41no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—41no—
189C2×C43⋊C8—41no—
190C2×C43⋊C8—41no—
191C2×C43⋊C8—41no—
192C23×C43—42no—
193C23×C43#11711yescharacteristic
194C23×C43#12111yescharacteristic
195C23×C43#12311yescharacteristic
196C23×C43#12311yescharacteristic
197C23×C43#12311yescharacteristic
198C23×C43#12411yescharacteristic
199C23×C43#12611yescharacteristic
200C22×D43—22no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—82no—
204C2×C4×C43—42no—
205C2×C4×C43—82no—
206C2×C4×C43C2×C22⋊C411yescharacteristic
207C2×C4×C43#11711yescharacteristic
208C2×C4×C43C4×D411yescharacteristic
209C2×C4×C43C4×D411yescharacteristic
210C2×C4×C43C4×D411yescharacteristic
211C2×C4×C43C4×D411yescharacteristic
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#12011yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12311yescharacteristic
222C2×C4×C43#12311yescharacteristic
223C2×C4×C43#12311yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×C4×C43#12311yescharacteristic
227C2×C4×C43#12311yescharacteristic
228C2×C4×C43#12411yescharacteristic
229C2×C4×C43#12411yescharacteristic
230C2×C4×C43#12411yescharacteristic
231C2×C4×C43#12611yescharacteristic
232C2×C4×C43#12611yescharacteristic
233C2×C4×C43#12611yescharacteristic
234C22⋊D43—42no—
235C22⋊D43—42no—
236C22⋊D43—42no—
237C22⋊D43—42no—
238C2×Dic43—24no—
239C2×Dic43—22no—
240C2×Dic43—42no—
241C2×Dic43—44no—
242C2×Dic43—44no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246D172—22no—
247D172—22no—
248D172—41no—
249D172—41no—
250C4×D43—42no—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—42no—
254Dic86—22no—
255Dic86—22no—
256Dic86—41no—
257Dic86—41no—
258C8×C43—42no—
259C8×C43—42no—
260C43⋊C8—42no—
261C43⋊C8—42no—
262#11165—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43#38111yescharacteristic
271C22×C43#38811yescharacteristic
272C22×C43#38811yescharacteristic
273C22×C43#39411yescharacteristic
274C22×C43#39411yescharacteristic
275C22×C43#39711yescharacteristic
276C22×C43#39711yescharacteristic
277C2×D43—42no—
278C2×D43—82no—
279C2×D43—82no—
280C2×D43—82no—
281C4×C43—82no—
282C4×C43#38611yescharacteristic
283C4×C43#38611yescharacteristic
284C4×C43#38811yescharacteristic
285C4×C43#38811yescharacteristic
286C4×C43#39411yescharacteristic
287C4×C43#39411yescharacteristic
288C4×C43#39711yescharacteristic
289C4×C43#39711yescharacteristic
290Dic43—44no—
291Dic43—42no—
292C2×#421—431no—
293C22×#104—431no—
294C2×#413—431no—
295C2×#344D4311yescharacteristic, complemented
296#1738—431no—
297C2×#339—431no—
298#1728—431no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43#144011yescharacteristic
306C2×C43#193212yes—
307D43—82no—
308C22×#41—431no—
309C22×M16—431no—
310C22×M16—431no—
311C22×M16C2×D4311yescharacteristic
312C22×M16C2×D4311yescharacteristic
313C2×#117C2×D4311yescharacteristic
314C22×C42—431no—
315#421—862no—
316#421—862no—
317C2×#104—862no—
318C2×#104—862no—
319C2×#104—862no—
320C2×#104—862no—
321#413—862no—
322#413—862no—
323C2×#101—432no—
324C2×#100—432no—
325#344—22no—
326#341—862no—
327#339—862no—
328#336—862no—
329C43#1116511yescharacteristic, complemented, Sylow
330C2×#41—432no—
331C2×#41—432no—
332C2×#41—861no—
333C2×#41—861no—
334C2×#41—861no—
335C2×#41—861no—
336C2×#41—861no—
337C2×#41—861no—
338C2×#41—861no—
339C2×#41—861no—
340C2×#41—861no—
341C2×#41—861no—
342C22×Q8—431no—
343C22×D4—431no—
344C22×D4—861no—
345C23×C4—861no—
346C23×C4—861no—
347C23×C4C22×D4311yescharacteristic
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—432no—
359C2×M16—432no—
360C2×M16—861no—
361C2×M16—861no—
362C2×M16—861no—
363C2×M16—861no—
364C2×M16—861no—
365C2×M16—861no—
366C2×M16—861no—
367C2×M16—861no—
368C2×M16—861no—
369C2×M16—861no—
370C2×M16C4×D4312yes—
371C2×M16C22⋊D4312yes—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—861no—
375C22×C8—861no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117D17212yes—
380C2×C4⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42—21no—
383C2×C42—432no—
384C2×C42—861no—
385C2×C42—861no—
386C2×C42—861no—
387C2×C42—861no—
388C2×C42—861no—
389#104—868no—
390#104—868no—
391#101—864no—
392#100—864no—
393C24—861no—
394C24#1062189811yescharacteristic
395#41—862no—
396#41—862no—
397#41—862no—
398#41—862no—
399#41—862no—
400#41—862no—
401#41—862no—
402#41—862no—
403#41—1721no—
404#41—1721no—
405#41—1721no—
406#41—1721no—
407#41—1721no—
408#41—1721no—
409#41—1721no—
410#41—1721no—
411C2×Q8—432no—
412C2×Q8—861no—
413C2×Q8—861no—
414C2×Q8—861no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×D4—432no—
418C2×D4—862no—
419C2×D4—862no—
420C2×D4—861no—
421C2×D4—861no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—1721no—
426C2×D4—1721no—
427C2×D4—1721no—
428C2×D4—1721no—
429C22×C4—41no—
430C22×C4—861no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—1724no—
435C22×C4—1721no—
436C22×C4—1721no—
437C22×C4—1721no—
438C22×C4—1721no—
439C22×C4—1721no—
440C22×C4—1721no—
441C22×C4C2×C4×D4311yescharacteristic
442C22×C4C2×D17211yescharacteristic
443C22×C4#1062189811yescharacteristic
444C22×C4#1062189811yescharacteristic
445C22×C4#1062189811yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4D4×D4311yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4#1062190011yescharacteristic
451C22×C4#1062190011yescharacteristic
452C22×C4#1062190211yescharacteristic
453C22×C4#1062190211yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455M16—22no—
456M16—22no—
457M16—22no—
458M16—22no—
459M16—41no—
460M16—41no—
461M16—41no—
462M16—41no—
463M16—862no—
464M16—862no—
465M16—862no—
466M16—862no—
467M16—1721no—
468M16—1721no—
469M16—1721no—
470M16—1721no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—862no—
478C2×C8—862no—
479C2×C8—1721no—
480C2×C8—1721no—
481C2×C8—1721no—
482C2×C8—1721no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C22⋊C4—22no—
486C22⋊C4—41no—
487C42—22no—
488C42—41no—
489C42—862no—
490C42—862no—
491C42—1721no—
492C42—1721no—
493C23—42no—
494C23—862no—
495C23—3442no—
496C23—1721no—
497C23—1721no—
498C23#1306328211yescharacteristic
499C23#1306329911yescharacteristic
500C23#1306330711yescharacteristic
501C23#1306331011yescharacteristic
502C23#1306331011yescharacteristic
503C23#1306331111yescharacteristic
504C23#1306331911yescharacteristic
505Q8—862no—
506Q8—862no—
507Q8—1721no—
508Q8—1721no—
509D4—862no—
510D4—862no—
511D4—1722no—
512D4—1722no—
513D4—1722no—
514D4—1722no—
515D4—1721no—
516D4—1721no—
517C2×C4—42no—
518C2×C4—82no—
519C2×C4—864no—
520C2×C4—862no—
521C2×C4—1722no—
522C2×C4—1724no—
523C2×C4—1724no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4C22⋊C4×D4311yescharacteristic
532C2×C4#1306328311yescharacteristic
533C2×C4(C22⋊D43)⋊C411yescharacteristic
534C2×C4C4×C22⋊D4311yescharacteristic
535C2×C4#1306328711yescharacteristic
536C2×C4C4×D17211yescharacteristic
537C2×C4#1306329311yescharacteristic
538C2×C4#1306329511yescharacteristic
539C2×C4#1306329611yescharacteristic
540C2×C4#1306329711yescharacteristic
541C2×C4#1306329811yescharacteristic
542C2×C4#1306329811yescharacteristic
543C2×C4#1306329811yescharacteristic
544C2×C4#1306330011yescharacteristic
545C2×C4#1306330011yescharacteristic
546C2×C4#1306330711yescharacteristic
547C2×C4#1306330711yescharacteristic
548C2×C4#1306330811yescharacteristic
549C2×C4#1306330911yescharacteristic
550C2×C4#1306331011yescharacteristic
551C2×C4#1306331011yescharacteristic
552C2×C4#1306331011yescharacteristic
553C2×C4#1306331111yescharacteristic
554C2×C4#1306331311yescharacteristic
555C2×C4#1306331411yescharacteristic
556C2×C4#1306332011yescharacteristic
557C2×C4#1306332011yescharacteristic
558C2×C4#1306332011yescharacteristic
559C8—42no—
560C8—42no—
561C8—1722no—
562C8—1722no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—3442no—
571C22—3442no—
572C22—3442no—
573C22—1722no—
574C22#1458276111yescharacteristic
575C22#1458278811yescharacteristic
576C22#1458279011yescharacteristic
577C22#1458281511yescharacteristic
578C22#1458281611yescharacteristic
579C22#1458282811yescharacteristic
580C22#1458282811yescharacteristic
581C4—82no—
582C4—1724no—
583C4—1722no—
584C4#1458277511yescharacteristic
585C4#1458277711yescharacteristic
586C4#1458278911yescharacteristic
587C4#1458279111yescharacteristic
588C4#1458281411yescharacteristic
589C4#1458281711yescharacteristic
590C4#1458282511yescharacteristic
591C4#1458282611yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—3442no—
599C2#1913284311yescharacteristic
600C2#1913526212yes—
subgroupG/H
centerC2×C4#13063298
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC22×C43#388
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#11165
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. #19134321C2semidirect
5. C2×#14582658C2semidirect
6. #19134288C2semidirect
7. C2×C43×#344C2semidirect
20. C2×#13063243C4semidirect
21. C2×#13063241C4semidirect
295. C2×#344D43semidirect
329. C43#11165semidirect

Maximal subgroups

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

subgroupindex
C2×#145829172
C22×#130632512
C2×#145828812
#191343212
C2×#145826582
#191342882
C2×C43×#3442
#1116543