Finite Group Databasebeta

← #25164701

Subgroups — #25164701

Order 11008.

748 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138936C211yesmaximal, characteristic
2#19137598C211yesmaximal, characteristic
3#19135918C211yesmaximal, characteristic, complemented
4#19135792C211yesmaximal, characteristic
5#19135747C211yesmaximal, characteristic, complemented
6#19135605C211yesmaximal, characteristic
7#19135550C211yesmaximal, characteristic, complemented
8#19135271C211yesmaximal, characteristic, complemented
9#19135230C211yesmaximal, characteristic, complemented
10#19135181C211yesmaximal, characteristic, complemented
11#19134935C211yesmaximal, characteristic, complemented
12#19134900C211yesmaximal, characteristic
13#19134682C211yesmaximal, characteristic
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29#14582840—21no—
30#14582827—21no—
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582796—21no—
36#14582787—21no—
37#14582786—21no—
38#14582771—21no—
39#14582763—21no—
40#14582759C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C23×Dic43—21no—
62C2×Dic172—22no—
63C2×Dic172—41no—
64C2×Dic172—41no—
65#13063317—22no—
66#13063317—41no—
67#13063304—22no—
68#13063304—22no—
69#13063304—22no—
70#13063304—41no—
71C4×Dic86—22no—
72C4×Dic86—41no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—41no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94#13063257—22no—
95#13063250—22no—
96#13063250—22no—
97#13063250—22no—
98#13063250—22no—
99#13063250—41no—
100#13063250—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C23×C4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C4⋊C8×C43—41no—
121C22⋊C8×C43—41no—
122C22⋊C8×C43—41no—
123C4×C8×C43—41no—
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43C2×D411yescharacteristic
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43—81no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86#4112yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C22⋊Dic43—24no—
181C22⋊Dic43—42no—
182C22⋊Dic43—42no—
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—42no—
193C4⋊Dic43#4112yes—
194C4⋊Dic43#4112yes—
195C4⋊Dic43#4112yes—
196Dic43⋊C4—24no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—81no—
202C4×Dic43—42no—
203C4×Dic43—42no—
204C4×Dic43—81no—
205Dic172—44no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43#13512yes—
213C23×C43C22×D411yescharacteristic
214C2×C4×C43—21no—
215C2×C4×C43—21no—
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×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#13712yes—
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
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—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—84no—
264Dic86—22no—
265Dic86—22no—
266Dic86—41no—
267Dic86—41no—
268Dic86—41no—
269Dic86—41no—
270Dic86—41no—
271Dic86—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276#26725—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43#52511yescharacteristic
285C22×C43#54611yescharacteristic
286C22×C43#54611yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43C2×#13711yescharacteristic
289C22×C43#57711yescharacteristic
290C22×C43#57811yescharacteristic
291C4×C43—22no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43#52911yescharacteristic
297C4×C43#53811yescharacteristic
298C4×C43#55511yescharacteristic
299C4×C43#55911yescharacteristic
300Dic43—42no—
301Dic43—42no—
302Dic43—42no—
303Dic43—42no—
304Dic43—81no—
305Dic43—81no—
306Dic43—81no—
307Dic43—81no—
308#2489—431no—
309#2360—431no—
310#2056—431no—
311#2035—431no—
312#2026—431no—
313#2001—431no—
314#1989—431no—
315#1933—431no—
316#1927—431no—
317#1923D4311yescharacteristic
318#1920—431no—
319#1878—431no—
320#1872—431no—
321#1823—431no—
322C4×#103—431no—
323C2×C43—42no—
324C2×C43#245911yescharacteristic
325C2×C43#310811yescharacteristic
326C2×C43#312011yescharacteristic
327C2×C43#329611yescharacteristic
328C2×C43#330011yescharacteristic
329C2×C43#331211yescharacteristic
330C2×C43#333111yescharacteristic
331C22×Q16—431no—
332C2×#125—431no—
333C2×C22⋊Q8—431no—
334C2×C22⋊Q8—431no—
335C2×C4×Q8—431no—
336C22×C4⋊C4—431no—
337C2×#106—431no—
338C2×C4⋊C8C2×D4311yescharacteristic
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×C22⋊C8C2×D4311yescharacteristic
346C2×C22⋊C8C2×D4311yescharacteristic
347C2×C4×C8C2×D4311yescharacteristic
348#400—861no—
349#397—861no—
350#391—431no—
351#391—431no—
352#391—431no—
353#389—431no—
354#389—861no—
355#388—861no—
356#387—861no—
357#385—861no—
358#382—861no—
359#380—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—431no—
362C4×C22⋊C4—861no—
363C4×C22⋊C4C2×D4311yescharacteristic
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#336C2×D4311yescharacteristic
373#336C2×D4311yescharacteristic
374C43#2672511yescharacteristic, complemented, Sylow
375C22×Q8—431no—
376C22×Q8—431no—
377C23×C4—861no—
378C23×C4C22×D4311yescharacteristic
379C2×Q16—862no—
380C2×Q16—1721no—
381C2×Q16—1721no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384C22×C8C22×D4311yescharacteristic
385C22×C8C22×D4311yescharacteristic
386#125—862no—
387#125—1721no—
388C22⋊Q8—862no—
389C22⋊Q8—862no—
390C22⋊Q8—862no—
391C22⋊Q8—1721no—
392C4×Q8—862no—
393C4×Q8—1721no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—1721no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4D17211yescharacteristic
413C2×C22⋊C4D17211yescharacteristic
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418C2×C42C22×D4311yescharacteristic
419#106—862no—
420C4⋊C8—41no—
421#103—862no—
422#103—862no—
423#103—862no—
424#103—862no—
425#103—1721no—
426#103—1721no—
427C22⋊C8—41no—
428C22⋊C8—41no—
429C4×C8—41no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95D17211yescharacteristic
441#95D17211yescharacteristic
442C24C2×D17211yescharacteristic
443C2×Q8—432no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—3441no—
470C22×C4—1722no—
471C22×C4—1722no—
472C22×C4C2×D17211yescharacteristic
473C22×C4C2×D17211yescharacteristic
474C22×C4C2×D17211yescharacteristic
475C22×C4C2×D17211yescharacteristic
476C22×C4C2×D17211yescharacteristic
477C22×C4C23×D4311yescharacteristic
478Q16—1724no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C4⋊C4—432no—
492C4⋊C4—432no—
493C4⋊C4—432no—
494C4⋊C4—864no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—3441no—
505C4⋊C4—1722no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—864no—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—3441no—
520C42—1722no—
521C42—1722no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23#1306334712yes—
529C23C22×D17211yescharacteristic
530Q8—862no—
531Q8—862no—
532Q8—1721no—
533Q8—1721no—
534Q8—1721no—
535Q8—1721no—
536Q8—1721no—
537Q8—1721no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—3444no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4#1306335812yes—
582C2×C4#41×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4#41×D4311yescharacteristic
586C2×C4#1306337011yescharacteristic
587C2×C4#1306337011yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22#1458341111yescharacteristic
600C22#1458354411yescharacteristic
601C22#1458354411yescharacteristic
602C22C2×#1306334711yescharacteristic
603C22C2×#1306335811yescharacteristic
604C22#1458371111yescharacteristic
605C22#1458371611yescharacteristic
606C4—22no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—3441no—
612C4—3441no—
613C4—3441no—
614C4—3441no—
615C4—1722no—
616C4—1722no—
617C4—1722no—
618C4—1722no—
619C4#1458343211yescharacteristic
620C4#1458348111yescharacteristic
621C4#1458361111yescharacteristic
622C4#1458363311yescharacteristic
623C2—42no—
624C2#1913853011yescharacteristic
625C2#1914467711yescharacteristic
626C2#1914481111yescharacteristic
627C2#1914643211yescharacteristic
628C2#1914648411yescharacteristic
629C2#1914664811yescharacteristic
630C2#1914691211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1923C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1923D43
hypocenterC43#26725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
3. #19135918C2semidirect
5. #19135747C2semidirect
7. #19135550C2semidirect
8. #19135271C2semidirect
9. #19135230C2semidirect
10. #19135181C2semidirect
11. #19134935C2semidirect
14. C4×#13063250C2semidirect
374. C43#26725semidirect

Maximal subgroups

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

subgroupindex
#191389362
#191375982
#191359182
#191357922
#191357472
#191356052
#191355502
#191352712
#191352302
#191351812
#191349352
#191349002
#191346822
C4×#130632502
C43×#19232
#2672543