Finite Group Databasebeta

← #25196748

Subgroups — #25196748

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140416C211yesmaximal, characteristic
2#19137277C211yesmaximal, characteristic
3#19136164C211yesmaximal, characteristic, complemented
4#19136142C211yesmaximal, characteristic, complemented
5#19135929C211yesmaximal, characteristic, complemented
6#19135737C211yesmaximal, characteristic, complemented
7#19135188C211yesmaximal, characteristic, complemented
8#19135181C211yesmaximal, characteristic, complemented
9#19135028C211yesmaximal, characteristic
10#19135018C211yesmaximal, characteristic
11#19134866C211yesmaximal, characteristic, complemented
12#19134866C211yesmaximal, characteristic, complemented
13#19134628C211yesmaximal, characteristic
14#19134620C211yesmaximal, characteristic
15C43×#1729C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27#14582838—21no—
28#14582835—21no—
29#14582819—21no—
30#14582811—21no—
31#14582805C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582794—21no—
36#14582793—21no—
37#14582787—21no—
38#14582780—21no—
39#14582765C2211yescharacteristic
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C22×M16×C43C2211yescharacteristic
53C23×C8×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×Dic86C2311yescharacteristic
61#13063325—41no—
62#13063325—41no—
63#13063304—22no—
64#13063304Q814yescomplemented
65C4×Dic86—41no—
66C4×Dic86—41no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063259—22no—
87#13063257—22no—
88#13063257—41no—
89#13063257—41no—
90#13063250—22no—
91#13063250—22no—
92#13063250—41no—
93#13063250—41no—
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—
105C23×C4×C43C2311yescharacteristic
106C2×M16×C43—22no—
107C2×M16×C43—22no—
108C2×M16×C43—41no—
109C22×C8×C43—22no—
110C22×C8×C43—22no—
111C22×C8×C43—41no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#117×C43—41no—
117#117×C43—41no—
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C22⋊C4×C43D411yescharacteristic
121C2×C22⋊C4×C43D411yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C24×C43C2×D411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×Q812yes—
135C22×C4×C43#4112yes—
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—42no—
151C2×Dic86—81no—
152C2×Dic86—81no—
153C2×Dic86C2×Q812yes—
154M16×C43—44no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—44no—
166C2×C8×C43#4112yes—
167C2×C8×C43#4112yes—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—21no—
176C22⋊Dic43—24no—
177C22⋊Dic43—81no—
178C22⋊Dic43—81no—
179C22⋊Dic43—81no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—42no—
194C4⋊Dic43C2×Q812yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—42no—
197Dic43⋊C4—81no—
198Dic43⋊C4—81no—
199Dic43⋊C4—81no—
200C4×Dic43—42no—
201C4×Dic43—81no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C22⋊Q812yes—
209C23×C43C22×D411yescharacteristic
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43C22⋊Q812yes—
229C2×C4×C43C22×Q811yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43H(5,𝔽2)11yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259Dic86—22no—
260Dic86—22no—
261Dic86—41no—
262Dic86—41no—
263Dic86—84no—
264C8×C43—22no—
265C8×C43—22no—
266C8×C43—41no—
267C8×C43—41no—
268#29170—431nomaximal, Sylow
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43C2×C22⋊Q811yescharacteristic
277C22×C43#53211yescharacteristic
278C22×C43#53411yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57711yescharacteristic
282C22×C43#57811yescharacteristic
283C4×C43—22no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43#55111yescharacteristic
289C4×C43#55111yescharacteristic
290C4×C43#55411yescharacteristic
291C4×C43#55411yescharacteristic
292Dic43—42no—
293Dic43—42no—
294Dic43—81no—
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300#2628—431no—
301#2323—431no—
302#2101—431no—
303#2097—431no—
304#2058—431no—
305#2024—431no—
306#1921—431no—
307#1920—431no—
308#1894—431no—
309#1892—431no—
310#1865—431no—
311#1865—431no—
312#1809—431no—
313#1807—431no—
314#1729D4311yescharacteristic
315C2×C43—42no—
316C2×C43#256411yescharacteristic
317C2×C43#308211yescharacteristic
318C2×C43#308411yescharacteristic
319C2×C43#317311yescharacteristic
320C2×C43#317811yescharacteristic
321C2×C43#320011yescharacteristic
322C2×C43#320111yescharacteristic
323C22×M16C2×D4311yescharacteristic
324C23×C8C2×D4311yescharacteristic
325C2×C4⋊Q8—431no—
326C2×C22⋊Q8—431no—
327C2×C4×Q8—431no—
328C2×#117C2×D4311yescharacteristic
329C2×#107—431no—
330C2×#106—431no—
331C2×#106—431no—
332C2×#106—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#103—431no—
337#400—861no—
338#399—861no—
339#395—861no—
340#393—861no—
341#391—431no—
342#389—431no—
343#389—431no—
344#389—431no—
345#389—861no—
346#388—861no—
347#388—861no—
348#387—861no—
349#382—431no—
350#380—431no—
351#380—431no—
352#380—431no—
353C4×C4⋊C4—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#336C2×D4311yescharacteristic
363#336C2×D4311yescharacteristic
364#336C2×D4311yescharacteristic
365#336C2×D4311yescharacteristic
366C43#2917011yescharacteristic, complemented, Sylow
367C22×Q8—431no—
368C22×Q8—861no—
369C23×C4C22×D4311yescharacteristic
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—41no—
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—41no—
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380C4⋊Q8—1721no—
381C4⋊Q8—1721no—
382C22⋊Q8—434no—
383C22⋊Q8—862no—
384C4×Q8—1721no—
385C4×Q8—1721no—
386#117—41no—
387#117—41no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4D17211yescharacteristic
402C2×C4⋊C4D17211yescharacteristic
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4D17211yescharacteristic
408C2×C22⋊C4D17211yescharacteristic
409C2×C42—861no—
410C2×C42—861no—
411C2×C42C22×D4311yescharacteristic
412C2×C42C22×D4311yescharacteristic
413#107—862no—
414#106—862no—
415#106—1721no—
416#106—1721no—
417#103—862no—
418#103—862no—
419#103—1721no—
420#103—1721no—
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—
430#95—861no—
431#95—861no—
432C24C2×D17211yescharacteristic
433C2×Q8—432no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—3441no—
440C2×Q8—3441no—
441C2×Q8—1722no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4C2×D17211yescharacteristic
455C22×C4C2×D17211yescharacteristic
456C22×C4C2×D17211yescharacteristic
457C22×C4C2×D17211yescharacteristic
458C22×C4C2×D17211yescharacteristic
459C22×C4#1062190012yes—
460C22×C4Q8×D4312yes—
461C22×C4C23×D4311yescharacteristic
462M16—44no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—44no—
474C2×C8#1062189812yes—
475C2×C8#1062189812yes—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—432no—
479C4⋊C4—864no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C4⋊C4—3441no—
496C4⋊C4—1722no—
497C4⋊C4—1722no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—864no—
501C22⋊C4—3441no—
502C22⋊C4—3441no—
503C22⋊C4—3441no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—3441no—
509C42—1722no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23#1306330512yes—
517C23C22×D17211yescharacteristic
518Q8—862no—
519Q8—862no—
520Q8—3444no—
521Q8—1721no—
522Q8—1721no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
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—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4#1306330512yes—
566C2×C4C2×Q8×D4311yescharacteristic
567C2×C4C2×#1062190011yescharacteristic
568C2×C4C2×#1062189811yescharacteristic
569C2×C4C2×#1062189811yescharacteristic
570C2×C4#1306337011yescharacteristic
571C2×C4#1306337011yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×#1306330511yescharacteristic
584C22#1458344911yescharacteristic
585C22#1458346111yescharacteristic
586C22#1458371111yescharacteristic
587C22#1458371111yescharacteristic
588C22#1458371111yescharacteristic
589C22#1458371611yescharacteristic
590C4—22no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—3441no—
596C4—3441no—
597C4—3441no—
598C4—3441no—
599C4—3441no—
600C4—3441no—
601C4—1722no—
602C4—1722no—
603C4#1458357511yescharacteristic
604C4#1458357511yescharacteristic
605C4#1458360411yescharacteristic
606C4#1458360411yescharacteristic
607C2—42no—
608C2#1913977511yescharacteristic
609C2#1914443811yescharacteristic
610C2#1914445911yescharacteristic
611C2#1914521211yescharacteristic
612C2#1914526311yescharacteristic
613C2#1914546811yescharacteristic
614C2#1914547911yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1729C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1729D43
hypocenterC43#29170
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1729

Complements

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

NH ≅ G/Ntype
3. #19136164C2semidirect
4. #19136142C2semidirect
5. #19135929C2semidirect
6. #19135737C2semidirect
7. #19135188C2semidirect
8. #19135181C2semidirect
11. #19134866C2semidirect
12. #19134866C2semidirect
64. #13063304Q8semidirect
366. C43#29170semidirect

Maximal subgroups

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

subgroupindex
#191404162
#191372772
#191361642
#191361422
#191359292
#191357372
#191351882
#191351812
#191350282
#191350182
#191348662
#191346282
#191346202
C43×#17292
#2917043