Finite Group Databasebeta

← #25199790

Subgroups — #25199790

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140560C211yesmaximal, characteristic, complemented
2#19137239C211yesmaximal, characteristic
3#19136093C211yesmaximal, characteristic, complemented
4#19135975C211yesmaximal, characteristic, complemented
5#19135968C211yesmaximal, characteristic
6#19135913C211yesmaximal, characteristic
7#19135449C211yesmaximal, characteristic
8#19135323C211yesmaximal, characteristic, complemented
9#19135292C211yesmaximal, characteristic
10#19135285C211yesmaximal, characteristic, complemented
11#19135230C211yesmaximal, characteristic, complemented
12#19135174C211yesmaximal, characteristic, complemented
13#19134928C211yesmaximal, characteristic
14#19134859C211yesmaximal, characteristic
15C43×#1768C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063257C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063250C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C43⋊#401—21no—
28#14582840—21no—
29#14582840—21no—
30#14582840—21no—
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582788—21no—
42#14582788—21no—
43#14582761—21no—
44#14582758—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C43×#376C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621873—22no—
63C2×#10621873—22no—
64C2×#10621873—41no—
65C4×D172—22no—
66C4×D172—22no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84#13063257—22no—
85#13063257—22no—
86#13063257—41no—
87#13063250—22no—
88#13063250—22no—
89#13063250—41no—
90#13063247—22no—
91#13063247—22no—
92#13063247—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
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—
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111C2×C42×C43C2311yescharacteristic
112C4⋊C8×C43—22no—
113C4⋊C8×C43—22no—
114#97×C43—41no—
115C4×C8×C43—41no—
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C23×D43—21no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172#4112yes—
141C2×C4×D43—24no—
142C2×C4×D43—81no—
143C2×C4×D43—81no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43#4112yes—
161C2×C8×C43#4112yes—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—21no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—81no—
170(C2×D43)⋊C4—81no—
171(C2×D43)⋊C4—81no—
172(C2×D43)⋊C4—81no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43#4112yes—
185Dic43⋊C4—81no—
186Dic43⋊C4—81no—
187Dic43⋊C4—81no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190C4×Dic43—81no—
191#10621873—44no—
192C23×C43C22×D411yescharacteristic
193C22×D43—22no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43H(5,𝔽2)11yescharacteristic
223C2×C4×C432−1+411yescharacteristic
224C2×Dic43—22no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245D172—22no—
246D172—22no—
247D172—41no—
248D172—41no—
249C4×D43—84no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254C8×C43—22no—
255C8×C43—22no—
256C8×C43—41no—
257C8×C43—41no—
258#29440—431nomaximal, Sylow
259C22×C43#52511yescharacteristic
260C22×C43#53211yescharacteristic
261C22×C43#53711yescharacteristic
262C22×C43#57711yescharacteristic
263C22×C43#57711yescharacteristic
264C22×C43#57711yescharacteristic
265C22×C43#57711yescharacteristic
266C2×D43—42no—
267C2×D43—42no—
268C2×D43—42no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43#55111yescharacteristic
280C4×C43#55211yescharacteristic
281C4×C43#55311yescharacteristic
282C4×C43#55611yescharacteristic
283Dic43—42no—
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289Dic43—81no—
290#2645—431no—
291#2319—431no—
292#2088—431no—
293#2066—431no—
294#2065—431no—
295#2055—431no—
296#1968—431no—
297#1941—431no—
298#1936—431no—
299#1935—431no—
300#1927—431no—
301#1919—431no—
302#1877—431no—
303#1864—431no—
304#1768D4311yescharacteristic, complemented
305C2×C43#260111yescharacteristic
306C2×C43#312311yescharacteristic
307C2×C43#312511yescharacteristic
308C2×C43#317311yescharacteristic
309C2×C43#317411yescharacteristic
310C2×C43#326011yescharacteristic
311C2×C43#326311yescharacteristic
312D43—82no—
313C22×SD16—431no—
314C2×C4×D4—431no—
315C2×#106—431no—
316C2×#106—431no—
317C2×#106—431no—
318C2×C4⋊C8C2×D4311yescharacteristic
319C2×C4⋊C8C2×D4311yescharacteristic
320C2×#103—431no—
321C2×#103—431no—
322C2×#103—431no—
323C2×#102—431no—
324C2×#102—431no—
325C2×#102—431no—
326C2×#97C2×D4311yescharacteristic
327C2×C4×C8C2×D4311yescharacteristic
328#401—861no—
329#400—861no—
330#400—861no—
331#400—861no—
332#391—431no—
333#391—431no—
334#391—431no—
335#390—431no—
336#390—431no—
337#389—431no—
338#389—431no—
339#389—431no—
340#389—431no—
341#389—431no—
342#388—861no—
343#388—861no—
344#381—861no—
345#380—861no—
346C4×C4⋊C4—431no—
347#376C2×D4311yescharacteristic
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#336C2×D4311yescharacteristic
355#336C2×D4311yescharacteristic
356C43#2944011yescharacteristic, complemented, Sylow
357C22×Q8—431no—
358C22×D4—431no—
359C23×C4—861no—
360C2×SD16—862no—
361C2×SD16—862no—
362C2×SD16—1721no—
363C22×C8C22×D4311yescharacteristic
364C22×C8C22×D4311yescharacteristic
365C22×C8C22×D4311yescharacteristic
366C22×C8C22×D4311yescharacteristic
367C4×D4—862no—
368C4×D4—862no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C42—861no—
386C2×C42C22×D4311yescharacteristic
387C2×C42C22×D4311yescharacteristic
388C2×C42C22×D4311yescharacteristic
389#106—862no—
390#106—862no—
391#106—1721no—
392C4⋊C8—22no—
393C4⋊C8—22no—
394#103—862no—
395#103—862no—
396#103—1721no—
397#102—862no—
398#102—862no—
399#102—1721no—
400#97—41no—
401C4×C8—41no—
402#95—861no—
403#95—861no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95D17211yescharacteristic
415#95D17211yescharacteristic
416#95D17211yescharacteristic
417#95D17211yescharacteristic
418C24—861no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×D4—432no—
426C2×D4—861no—
427C2×D4—861no—
428C2×D4—861no—
429C2×D4—861no—
430C2×D4—861no—
431C22×C4—864no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—3441no—
440C22×C4—3441no—
441C22×C4C2×D17211yescharacteristic
442C22×C4C2×D17211yescharacteristic
443C22×C4C2×D17211yescharacteristic
444C22×C4C2×D17211yescharacteristic
445C22×C4C2×D17211yescharacteristic
446C22×C4C2×D17211yescharacteristic
447C22×C4C23×D4311yescharacteristic
448SD16—1724no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8#1062189812yes—
460C2×C8#1062189812yes—
461C4⋊C4—432no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—3441no—
474C4⋊C4—3441no—
475C4⋊C4—3441no—
476C4⋊C4—3441no—
477C4⋊C4—3441no—
478C22⋊C4—864no—
479C22⋊C4—3441no—
480C22⋊C4—3441no—
481C22⋊C4—3441no—
482C22⋊C4—3441no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—3441no—
490C23—862no—
491C23—1721no—
492C23—1721no—
493C23—1721no—
494C23—1721no—
495C23—1721no—
496C23—1721no—
497C23C22×D17211yescharacteristic
498Q8—1721no—
499Q8—1721no—
500Q8—1721no—
501Q8—1721no—
502D4—862no—
503D4—862no—
504D4—1721no—
505D4—1721no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—862no—
525C2×C4—3444no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4#41×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C2×C4C2×#1062189811yescharacteristic
549C2×C4C2×#1062189811yescharacteristic
550C2×C4#1306337011yescharacteristic
551C2×C4#1306337311yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C22—3441no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22—1722no—
561C22—1722no—
562C22—1722no—
563C22#1458341111yescharacteristic
564C22#1458344911yescharacteristic
565C22#1458348011yescharacteristic
566C22#1458371111yescharacteristic
567C22#1458371111yescharacteristic
568C22#1458371111yescharacteristic
569C22#1458371111yescharacteristic
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—3441no—
577C4—3441no—
578C4—3441no—
579C4—3441no—
580C4—3441no—
581C4—3441no—
582C4—1722no—
583C4#1458357811yescharacteristic
584C4#1458359011yescharacteristic
585C4#1458359811yescharacteristic
586C4#1458362111yescharacteristic
587C2—3442no—
588C2#1914018611yescharacteristic
589C2#1914484811yescharacteristic
590C2#1914487411yescharacteristic
591C2#1914521211yescharacteristic
592C2#1914522311yescharacteristic
593C2#1914604211yescharacteristic
594C2#1914606611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1768C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1768D43
hypocenterC43#29440
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
1. #19140560C2semidirect
3. #19136093C2semidirect
4. #19135975C2semidirect
8. #19135323C2semidirect
10. #19135285C2semidirect
11. #19135230C2semidirect
12. #19135174C2semidirect
15. C43×#1768C2semidirect
304. #1768D43semidirect
356. C43#29440semidirect

Maximal subgroups

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

subgroupindex
#191405602
#191372392
#191360932
#191359752
#191359682
#191359132
#191354492
#191353232
#191352922
#191352852
#191352302
#191351742
#191349282
#191348592
C43×#17682
#2944043