Finite Group Databasebeta

← #25146358

Subgroups — #25146358

Order 11008.

788 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583120C211yesmaximal, characteristic
2C2×#14583027C211yesmaximal, characteristic, complemented
3#19140080C211yesmaximal, characteristic
4#19139967C211yesmaximal, characteristic, complemented
5#19135973C211yesmaximal, characteristic, complemented
6#19135967C211yesmaximal, characteristic
7#19135919C211yesmaximal, characteristic, complemented
8#19135912C211yesmaximal, characteristic
9#19135466C211yesmaximal, characteristic, complemented
10#19135450C211yesmaximal, characteristic
11#19135410C211yesmaximal, characteristic
12#19135357C211yesmaximal, characteristic, complemented
13#19135269C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21#14583120—24no—
22#14583027—24no—
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36#14582833—21no—
37#14582830—21no—
38#14582827—21no—
39#14582811—21no—
40#14582805C2211yescharacteristic
41#14582805C2211yescharacteristic
42#14582804C2211yescharacteristic
43#14582804C2211yescharacteristic
44#14582803—21no—
45#14582802C2211yescharacteristic
46#14582795C2211yescharacteristic
47#14582794—21no—
48#14582792—21no—
49#14582787—21no—
50#14582768C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×Dic172—22no—
65C2×Dic172—22no—
66C2×Dic172—41no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063312—22no—
73#13063312—22no—
74C4×Dic86—22no—
75C4×Dic86—22no—
76#13063290—22no—
77#13063290—22no—
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D411yescharacteristic
86C2×Dic43⋊C4D411yescharacteristic
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063257—41no—
96#13063256—41no—
97C4⋊(C43⋊C8)—22no—
98Dic43⋊C8—22no—
99Dic43⋊C8D414yes—
100#13063250—22no—
101#13063250—22no—
102#13063248—22no—
103#13063248—22no—
104#13063248—41no—
105#13063246—41no—
106#13063235—22no—
107C8×Dic43—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C22×D4×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#102×C43—22no—
129#102×C43—22no—
130#97×C43—22no—
131#95×C43—21no—
132C24×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—22no—
159C2×Dic86—22no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—41no—
167C2×Dic86#4112yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D412yes—
173C2×C8×C43#4112yes—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—81no—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—81no—
183C42×C43—21no—
184C42×C43—21no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—81no—
189#10621883—44no—
190C4⋊Dic43—22no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200Dic43⋊C4—81no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—42no—
204C4×Dic43—81no—
205C4×Dic43C2×D412yes—
206C4×Dic43#4112yes—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8C2×D412yes—
213Dic172—44no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C22×D411yescharacteristic
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43#12112yes—
269C2×Dic43#12112yes—
270C2×Dic43#13712yes—
271Dic86—22no—
272Dic86—22no—
273Dic86—44no—
274Dic86—41no—
275Dic86—41no—
276Dic86—41no—
277Dic86—41no—
278Dic86—41no—
279Dic86—41no—
280C8×C43—22no—
281C8×C43—22no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284#25311—431nomaximal, Sylow
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43C2×#12111yescharacteristic
293C22×C43#54811yescharacteristic
294C22×C43#55011yescharacteristic
295C22×C43C2×#13711yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57711yescharacteristic
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43#52911yescharacteristic
305C4×C43#54211yescharacteristic
306C4×C43#54611yescharacteristic
307C4×C43#54811yescharacteristic
308Dic43—22no—
309Dic43—22no—
310Dic43—22no—
311Dic43—42no—
312Dic43—41no—
313Dic43—81no—
314Dic43—81no—
315Dic43—81no—
316C2×#464—431no—
317C2×#446—431no—
318#2592—431no—
319#2582—431no—
320#2066—431no—
321#2065—431no—
322#2056—431no—
323#2055—431no—
324#1971—431no—
325#1968—431no—
326#1959—431no—
327#1948—431no—
328#1936D4311yescharacteristic
329#1933—431no—
330#1763—431no—
331C2×C43—161no—
332C2×C43#242611yescharacteristic
333C2×C43#305611yescharacteristic
334C2×C43#306011yescharacteristic
335C2×C43#336911yescharacteristic
336C2×C43#337111yescharacteristic
337C2×C43#340011yescharacteristic
338C2×C43#340111yescharacteristic
339C22×Q16—431no—
340C22×SD16—431no—
341C2×#124—431no—
342C2×C4×Q8—431no—
343C2×C4×Q8—431no—
344#464—864no—
345#446—864no—
346C2×#106—431no—
347C2×#106—431no—
348C2×C4⋊C8—431no—
349C2×C4⋊C8—431no—
350C2×C4⋊C8—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#102—431no—
357C2×#102C2×D4311yescharacteristic
358C2×#102C2×D4311yescharacteristic
359C2×#97—431no—
360C2×#97C2×D4311yescharacteristic
361C2×C4×C8—431no—
362#398—861no—
363#398—861no—
364#397—861no—
365#393—861no—
366#391—431no—
367#391—431no—
368#391—431no—
369#391—431no—
370#391—861no—
371#390—431no—
372#390C2×D4311yescharacteristic
373#389—431no—
374#389—861no—
375#389C2×D4311yescharacteristic
376#388—861no—
377#388—861no—
378#384—431no—
379C4×C4⋊C4—431no—
380#340—431no—
381#340—431no—
382#340C2×D4311yescharacteristic
383#340C2×D4311yescharacteristic
384C43#2531111yescharacteristic, complemented, Sylow
385C22×Q8—431no—
386C22×Q8—431no—
387C22×Q8—431no—
388C22×D4C22×D4311yescharacteristic
389C2×Q16—862no—
390C2×Q16—862no—
391C2×Q16—1721no—
392C2×SD16—862no—
393C2×SD16—862no—
394C2×SD16—1721no—
395C22×C8—431no—
396C22×C8—431no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399#124—862no—
400#124—862no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—861no—
427C2×C42—861no—
428C2×C42C22×D4311yescharacteristic
429#106—1721no—
430#106—1721no—
431C4⋊C8—434no—
432C4⋊C8—862no—
433C4⋊C8—862no—
434#103—862no—
435#103—862no—
436#103—862no—
437#103—862no—
438#103—1721no—
439#102—22no—
440#102—22no—
441#102—1721no—
442#97—22no—
443#97—862no—
444C4×C8—862no—
445#95—21no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—21no—
457C2×Q8—432no—
458C2×Q8—862no—
459C2×Q8—862no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—1721no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492Q16—1724no—
493SD16—1724no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—432no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8#1062189812yes—
505C2×C8D4×D4312yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—81no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C22⋊C4—42no—
525C22⋊C4—81no—
526C22⋊C4—3441no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C42—21no—
531C42—21no—
532C42—432no—
533C42—432no—
534C42—861no—
535C42—861no—
536C42—3441no—
537C42—1722no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23C2×D4×D4311yescharacteristic
546Q8—862no—
547Q8—862no—
548Q8—1724no—
549Q8—1721no—
550Q8—1721no—
551Q8—1721no—
552Q8—1721no—
553Q8—1721no—
554Q8—1721no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—432no—
575C2×C4—432no—
576C2×C4—432no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4C2×D4×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4C2×#1062189811yescharacteristic
602C2×C4#1306337111yescharacteristic
603C2×C4#1306337211yescharacteristic
604C8—22no—
605C8—22no—
606C8—862no—
607C8—1721no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22#121×D4311yescharacteristic
616C22#1458355711yescharacteristic
617C22#1458357011yescharacteristic
618C22#137×D4311yescharacteristic
619C22#1458369511yescharacteristic
620C22#1458370911yescharacteristic
621C22#1458370911yescharacteristic
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—862no—
628C4—862no—
629C4—862no—
630C4—3441no—
631C4—3441no—
632C4—3441no—
633C4—1721no—
634C4—1722no—
635C4#1458342711yescharacteristic
636C4#1458351511yescharacteristic
637C4#1458354111yescharacteristic
638C4#1458355811yescharacteristic
639C2—161no—
640C2#1913816011yescharacteristic
641C2#1914422011yescharacteristic
642C2#1914425511yescharacteristic
643C2#1914733211yescharacteristic
644C2#1914735811yescharacteristic
645C2#1914764911yescharacteristic
646C2#1914766611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1936D43
hypocenterC43#25311
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. C2×#14583027C2semidirect
4. #19139967C2semidirect
5. #19135973C2semidirect
7. #19135919C2semidirect
9. #19135466C2semidirect
12. #19135357C2semidirect
13. #19135269C2semidirect
14. #19134424C2semidirect
384. C43#25311semidirect

Maximal subgroups

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

subgroupindex
C2×#145831202
C2×#145830272
#191400802
#191399672
#191359732
#191359672
#191359192
#191359122
#191354662
#191354502
#191354102
#191353572
#191352692
#191344242
C43×#19362
#2531143