Finite Group Databasebeta

← #25164746

Subgroups — #25164746

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138936C211yesmaximal, characteristic, complemented
2#19137631C211yesmaximal, characteristic
3#19135913C211yesmaximal, characteristic, complemented
4#19135785C211yesmaximal, characteristic
5#19135742C211yesmaximal, characteristic, complemented
6#19135600C211yesmaximal, characteristic
7#19135550C211yesmaximal, characteristic, complemented
8#19135271C211yesmaximal, characteristic, complemented
9#19135230C211yesmaximal, characteristic, complemented
10#19135181C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic, complemented
12#19134905C211yesmaximal, characteristic, complemented
13#19134691C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29#14582840—21no—
30#14582827—21no—
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582799—21no—
35#14582797C2211yescharacteristic
36#14582788—21no—
37#14582787—21no—
38#14582775—21no—
39#14582763—21no—
40#14582759C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582746—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×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C2×#10621873—22no—
64C2×#10621873—41no—
65C2×#10621873—41no—
66#13063317—22no—
67#13063317—41no—
68#13063304—22no—
69#13063304—41no—
70#13063299—22no—
71#13063299—22no—
72C4×D172—22no—
73C4×D172—41no—
74#13063284—22no—
75#13063284—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×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96#13063257—22no—
97#13063250—22no—
98#13063250—22no—
99#13063250—41no—
100#13063247—22no—
101#13063247—22no—
102#13063247—41no—
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
127C23×D43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C2×C22⋊D43—24no—
141C2×C22⋊D43—81no—
142C2×C22⋊D43—81no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172#4112yes—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—81no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—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—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C22⋊Dic43—42no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43#4112yes—
200C4⋊Dic43#4112yes—
201C4⋊Dic43#4112yes—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—81no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C4×Dic43—81no—
209#10621873—44no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43C22×D411yescharacteristic
218C22×D43—22no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C2×C4×C43—21no—
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—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43#13512yes—
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C22⋊D43—84no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
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—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272D172—22no—
273D172—22no—
274D172—41no—
275D172—41no—
276C4×D43—84no—
277Dic86—41no—
278Dic86—41no—
279Dic86—41no—
280Dic86—41no—
281C8×C43—41no—
282C8×C43—41no—
283C8×C43—41no—
284C8×C43—41no—
285#26728—431nomaximal, Sylow
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43#52511yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43#54611yescharacteristic
296C22×C43C2×#13511yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57711yescharacteristic
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C4×C43—22no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43#52911yescharacteristic
313C4×C43#53811yescharacteristic
314C4×C43#55511yescharacteristic
315C4×C43#55911yescharacteristic
316Dic43—42no—
317Dic43—42no—
318Dic43—42no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322Dic43—81no—
323#2489—431no—
324#2363—431no—
325#2055—431no—
326#2034—431no—
327#2025—431no—
328#2000—431no—
329#1989—431no—
330#1933—431no—
331#1927—431no—
332#1923D4311yescharacteristic, complemented
333#1920—431no—
334#1877—431no—
335#1873—431no—
336#1825—431no—
337C4×#102—431no—
338C2×C43—81no—
339C2×C43#245911yescharacteristic
340C2×C43#310211yescharacteristic
341C2×C43#312311yescharacteristic
342C2×C43#329611yescharacteristic
343C2×C43#330311yescharacteristic
344C2×C43#331711yescharacteristic
345C2×C43#332611yescharacteristic
346D43—82no—
347C22×SD16—431no—
348C2×#125—431no—
349C2×C22⋊Q8—431no—
350C2×#121—431no—
351C2×C4×D4—431no—
352C2×#117—431no—
353C2×#106—431no—
354C2×C4⋊C8C2×D4311yescharacteristic
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×C22⋊C8C2×D4311yescharacteristic
362C2×C22⋊C8C2×D4311yescharacteristic
363C2×C4×C8C2×D4311yescharacteristic
364#400—861no—
365#397—861no—
366#391—431no—
367#391—431no—
368#390—431no—
369#390—861no—
370#389—431no—
371#388—861no—
372#388—861no—
373#386—861no—
374#382—861no—
375#380—431no—
376C4×C4⋊C4—431no—
377C4×C4⋊C4—431no—
378C4×C22⋊C4—861no—
379C4×C22⋊C4C2×D4311yescharacteristic
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#336C2×D4311yescharacteristic
389#336C2×D4311yescharacteristic
390C43#2672811yescharacteristic, complemented, Sylow
391C22×Q8—431no—
392C22×D4—431no—
393C22×D4—861no—
394C23×C4—861no—
395C23×C4C22×D4311yescharacteristic
396C2×SD16—862no—
397C2×SD16—1721no—
398C2×SD16—1721no—
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403#125—862no—
404#125—1721no—
405C22⋊Q8—862no—
406C22⋊Q8—1721no—
407#121—862no—
408#121—862no—
409C4×D4—862no—
410C4×D4—1721no—
411#117—862no—
412#117—1721no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4D17211yescharacteristic
431C2×C22⋊C4D17211yescharacteristic
432C2×C42—861no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42C22×D4311yescharacteristic
436C2×C42C22×D4311yescharacteristic
437#106—862no—
438C4⋊C8—41no—
439#103—862no—
440#103—862no—
441#103—1721no—
442#102—862no—
443#102—862no—
444#102—1721no—
445C22⋊C8—41no—
446C22⋊C8—41no—
447C4×C8—41no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95D17211yescharacteristic
457#95D17211yescharacteristic
458C24—861no—
459C24C2×D17211yescharacteristic
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×D4—432no—
467C2×D4—864no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—3441no—
474C2×D4—3441no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—3441no—
489C22×C4—1722no—
490C22×C4—1722no—
491C22×C4C2×D17211yescharacteristic
492C22×C4C2×D17211yescharacteristic
493C22×C4C2×D17211yescharacteristic
494C22×C4C2×D17211yescharacteristic
495C22×C4C2×D17211yescharacteristic
496C22×C4C23×D4311yescharacteristic
497SD16—1724no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C4⋊C4—432no—
511C4⋊C4—432no—
512C4⋊C4—432no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—3441no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C22⋊C4—22no—
527C22⋊C4—41no—
528C22⋊C4—864no—
529C22⋊C4—3441no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—3441no—
540C42—1722no—
541C42—1722no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—862no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23C22×D17211yescharacteristic
557Q8—1721no—
558Q8—1721no—
559Q8—1721no—
560Q8—1721no—
561D4—862no—
562D4—862no—
563D4—3444no—
564D4—1721no—
565D4—1721no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—3444no—
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×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4#1306334712yes—
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#41×D4311yescharacteristic
611C2×C4#1306337011yescharacteristic
612C2×C4#1306337011yescharacteristic
613C8—41no—
614C8—41no—
615C8—41no—
616C8—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—3441no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22#1458341111yescharacteristic
632C22#1458354411yescharacteristic
633C22#1458354411yescharacteristic
634C22C2×#1306334711yescharacteristic
635C22#1458369911yescharacteristic
636C22#1458371111yescharacteristic
637C22#1458371111yescharacteristic
638C4—22no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—3441no—
644C4—3441no—
645C4—3441no—
646C4—3441no—
647C4—1722no—
648C4—1722no—
649C4—1722no—
650C4#1458343211yescharacteristic
651C4#1458348111yescharacteristic
652C4#1458361111yescharacteristic
653C4#1458363311yescharacteristic
654C2—81no—
655C2—3442no—
656C2#1913853011yescharacteristic
657C2#1914461511yescharacteristic
658C2#1914484811yescharacteristic
659C2#1914643211yescharacteristic
660C2#1914652411yescharacteristic
661C2#1914672311yescharacteristic
662C2#1914685011yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1923C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1923D43
hypocenterC43#26728
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
1. #19138936C2semidirect
3. #19135913C2semidirect
5. #19135742C2semidirect
7. #19135550C2semidirect
8. #19135271C2semidirect
9. #19135230C2semidirect
10. #19135181C2semidirect
11. #19134928C2semidirect
12. #19134905C2semidirect
13. #19134691C2semidirect
14. C4×#13063247C2semidirect
15. C43×#1923C2semidirect
332. #1923D43semidirect
390. C43#26728semidirect

Maximal subgroups

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

subgroupindex
#191389362
#191376312
#191359132
#191357852
#191357422
#191356002
#191355502
#191352712
#191352302
#191351812
#191349282
#191349052
#191346912
C4×#130632472
C43×#19232
#2672843