Finite Group Databasebeta

← #25100979

Subgroups — #25100979

Order 11008.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582997C211yesmaximal, characteristic
2#19137246C211yesmaximal, characteristic, complemented
3#19137233C211yesmaximal, characteristic
4#19135473C211yesmaximal, characteristic
5#19135446C211yesmaximal, characteristic
6#19135332C211yesmaximal, characteristic, complemented
7#19135327C211yesmaximal, characteristic, complemented
8#19135293C211yesmaximal, characteristic
9#19135282C211yesmaximal, characteristic, complemented
10#19135279C211yesmaximal, characteristic
11#19135268C211yesmaximal, characteristic, complemented
12#19134493C211yesmaximal, characteristic, complemented
13C4×#13063247C211yesmaximal, characteristic
14#19134281C211yesmaximal, characteristic, complemented
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18#14582997C418yescomplemented
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063236C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582806C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582790—21no—
40#14582790—21no—
41#14582785—21no—
42#14582785—21no—
43#14582767—21no—
44#14582765—21no—
45#14582761—21no—
46#14582758—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582745C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C4×D172—22no—
68C4×D172C2×C414yes—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063258—22no—
85#13063258C2×C414yes—
86#13063256—22no—
87#13063249C2×C414yes—
88#13063247—22no—
89#13063247—22no—
90#13063245C2×C414yes—
91#13063236C2×C414yes—
92#13063235—22no—
93#13063235—22no—
94C8×Dic43—22no—
95C8×Dic43—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C4×Q8×C43—22no—
113C4×Q8×C43C2×C414yes—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#103×C43—22no—
122#103×C43—22no—
123C4×C8×C43—22no—
124#95×C43—21no—
125C23×D43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C22×C412yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C22×C412yes—
152C2×C4×D43—24no—
153C2×C4×D43—81no—
154C2×C4×D43—81no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43#4112yes—
160C2×C8×C43#4112yes—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C22×C412yes—
168C42×C43—24no—
169C42×C43—81no—
170C42×C43C22×C412yes—
171C42×C43#4112yes—
172#10621884—28no—
173(C2×D43)⋊C4—24no—
174(C2×D43)⋊C4—81no—
175(C2×D43)⋊C4—81no—
176(C2×D43)⋊C4—81no—
177(C2×D43)⋊C4—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—81no—
184C4⋊Dic43—81no—
185C4⋊Dic43C22×C412yes—
186Dic43⋊C4—81no—
187Dic43⋊C4—81no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—81no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8C22×C412yes—
196C2×C43⋊C8C22×C412yes—
197C2×C43⋊C8#4112yes—
198C2×C43⋊C8#4112yes—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207Q8×C43—22no—
208Q8×C43—22no—
209Q8×C43—41no—
210Q8×C43—41no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C4×D412yes—
228C2×C4×C43C4×D412yes—
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×Dic43—22no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256D172—22no—
257D172—22no—
258D172—41no—
259D172—41no—
260C4×D43—84no—
261C8×C43—22no—
262C8×C43—22no—
263C43⋊C8—22no—
264C43⋊C8#11714yes—
265#21291—431nomaximal, Sylow
266C22×C43C2×C4×D411yescharacteristic
267C22×C43#53211yescharacteristic
268C22×C43#53211yescharacteristic
269C22×C43#57611yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57811yescharacteristic
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43C2×#11711yescharacteristic
287C4×C43C4×#4111yescharacteristic
288C4×C43#52911yescharacteristic
289C4×C43#52911yescharacteristic
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43—42no—
295Dic43—81no—
296Dic43—81no—
297C2×#440—431no—
298#2320—431no—
299#2319—431no—
300#1973—431no—
301#1968—431no—
302#1943—431no—
303#1942—431no—
304#1936—431no—
305#1935—431no—
306#1934—431no—
307#1933—431no—
308#1776—431no—
309C4×#103D4311yescharacteristic, complemented
310C4×#102—431no—
311#1726—431no—
312C2×C43#229311yescharacteristic
313C2×C43#294611yescharacteristic
314C2×C43#294711yescharacteristic
315C2×C43#317411yescharacteristic
316C2×C43#317511yescharacteristic
317C2×C43#317811yescharacteristic
318C2×C43#317911yescharacteristic
319D43—82no—
320C22×SD16—431no—
321C2×C4×Q8C2×D4311yescharacteristic
322C2×C4×D4—431no—
323#440—438no—
324C2×#107—431no—
325C2×#107—431no—
326C2×#106—431no—
327C2×#103—431no—
328C2×#103C2×D4311yescharacteristic
329C2×#103C2×D4311yescharacteristic
330C2×#102—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#97—431no—
334C2×#97—431no—
335C2×#97—431no—
336C2×C4×C8—431no—
337C2×C4×C8—431no—
338C2×C4×C8C2×D4311yescharacteristic
339#391—431no—
340#391—431no—
341#390—431no—
342#390—431no—
343#389—431no—
344#389—431no—
345#389—431no—
346#389—431no—
347#388—861no—
348#388—861no—
349#387—861no—
350#387—861no—
351#383—861no—
352#382—861no—
353#381—861no—
354#380—861no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4C2×D4311yescharacteristic
357#376—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340C2×D4311yescharacteristic
363#340C2×D4311yescharacteristic
364C43#2129111yescharacteristic, complemented, Sylow
365C22×Q8C22×D4311yescharacteristic
366C22×D4—431no—
367C23×C4—861no—
368C2×SD16—434no—
369C2×SD16—862no—
370C2×SD16—862no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375C4×Q8—22no—
376C4×Q8C4×D4314yes—
377C4×D4—434no—
378C4×D4—862no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#107—434no—
402#107—862no—
403#106—862no—
404#103—22no—
405#103—22no—
406#103—434no—
407#102—434no—
408#102—862no—
409#102—862no—
410#97—434no—
411#97—862no—
412#97—862no—
413C4×C8—22no—
414C4×C8—862no—
415C4×C8—862no—
416#95—21no—
417#95—431no—
418#95—431no—
419#95—431no—
420#95—431no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430C24—861no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×C4×D4312yes—
437C2×D4—432no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—864no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—3441no—
456C22×C4—3441no—
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460SD16—868no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—432no—
466C2×C8—432no—
467C2×C8—432no—
468C2×C8—432no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8#1062189812yes—
472C2×C8#1062189812yes—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—432no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—3441no—
486C4⋊C4—3441no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4C2×C4×D4312yes—
490C22⋊C4—864no—
491C22⋊C4—3441no—
492C22⋊C4—3441no—
493C22⋊C4—3441no—
494C22⋊C4—3441no—
495C42—24no—
496C42—81no—
497C42—861no—
498C42—861no—
499C42—861no—
500C42—861no—
501C42—3441no—
502C42C2×C4×D4312yes—
503C42#1062190012yes—
504C23—862no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23C2×D4×D4311yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—862no—
517D4—862no—
518D4—1721no—
519D4—1721no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—862no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—3444no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4(C22⋊D43)⋊C412yes—
559C2×C4(C22⋊D43)⋊C412yes—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#41×D4311yescharacteristic
563C2×C4C2×#1062190011yescharacteristic
564C2×C4C2×#1062189811yescharacteristic
565C2×C4C2×#1062189811yescharacteristic
566C8—22no—
567C8—22no—
568C8—434no—
569C8—862no—
570C22—3441no—
571C22—3441no—
572C22—3441no—
573C22—3441no—
574C22—1722no—
575C22—1722no—
576C22—1722no—
577C22C2×(C22⋊D43)⋊C411yescharacteristic
578C22#1458344611yescharacteristic
579C22#1458344611yescharacteristic
580C22#1458370111yescharacteristic
581C22#1458370511yescharacteristic
582C22#1458370611yescharacteristic
583C22#1458371211yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—3441no—
591C4—3441no—
592C4—1721no—
593C4—1722no—
594C4—1721no—
595C4—1721no—
596C4—1721no—
597C4#117×D4311yescharacteristic
598C4C4×#1062189811yescharacteristic
599C4#1458342911yescharacteristic
600C4#1458342911yescharacteristic
601C2—3442no—
602C2#1913705811yescharacteristic
603C2#1914343011yescharacteristic
604C2#1914343211yescharacteristic
605C2#1914521911yescharacteristic
606C2#1914523611yescharacteristic
607C2#1914526711yescharacteristic
608C2#1914527411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#103×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC4×#103D43
hypocenterC43#21291
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. #19137246C2semidirect
6. #19135332C2semidirect
7. #19135327C2semidirect
9. #19135282C2semidirect
11. #19135268C2semidirect
12. #19134493C2semidirect
14. #19134281C2semidirect
15. C4×#103×C43C2semidirect
18. #14582997C4semidirect
309. C4×#103D43semidirect
364. C43#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#145829972
#191372462
#191372332
#191354732
#191354462
#191353322
#191353272
#191352932
#191352822
#191352792
#191352682
#191344932
C4×#130632472
#191342812
C4×#103×C432
#2129143