Finite Group Databasebeta

← #25113876

Subgroups — #25113876

Order 11008.

934 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582909C211yesmaximal, characteristic
2#19137486C211yesmaximal, characteristic
3C22⋊C4×Dic86C211yesmaximal, characteristic
4#19135285C211yesmaximal, characteristic, complemented
5#19135271C211yesmaximal, characteristic, complemented
6#19135237C211yesmaximal, characteristic, complemented
7#19135230C211yesmaximal, characteristic, complemented
8#19134866C211yesmaximal, characteristic, complemented
9#19134852C211yesmaximal, characteristic, complemented
10#19134691C211yesmaximal, characteristic
11#19134628C211yesmaximal, characteristic
12#19134531C211yesmaximal, characteristic
13#19134426C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22#14582909C418yescomplemented
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582803—21no—
34#14582803—21no—
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582793—21no—
38#14582793—21no—
39#14582766—21no—
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582757—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582750—21no—
46C22⋊C4×Dic43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C4×C22⋊C4×C43C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86—22no—
61C22×Dic86—22no—
62C22×Dic86—21no—
63C22×Dic86—22no—
64C22×Dic86—41no—
65C22×Dic86—41no—
66C22×Dic86C2×C414yes—
67C22×Dic86C2311yescharacteristic
68C22×Dic86C2311yescharacteristic
69C23×Dic43—21no—
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×Dic86—41no—
73C4×Dic86—41no—
74#13063284—22no—
75#13063284C2×C414yes—
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×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94#13063259—41no—
95#13063257—41no—
96#13063250—22no—
97#13063250—22no—
98#13063250—41no—
99#13063250—41no—
100#13063250C2×C414yes—
101#13063250C2×C414yes—
102#13063250C2×C414yes—
103#13063250C2×C414yes—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C23×C4×C43C2311yescharacteristic
115C2×M16×C43—41no—
116C2×M16×C43—41no—
117C2×M16×C43C2×C414yes—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C22⋊C4×C43D411yescharacteristic
123C2×C22⋊C4×C43D411yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C22⋊C8×C43—22no—
127#97×C43—41no—
128C4×C8×C43—41no—
129#95×C43D411yescharacteristic
130#95×C43D411yescharacteristic
131C24×C43C2×D411yescharacteristic
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C22×C412yes—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43#4112yes—
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—24no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—28no—
163C2×Dic86—24no—
164C2×Dic86—21no—
165C2×Dic86—44no—
166C2×Dic86—44no—
167C2×Dic86—44no—
168C2×Dic86—42no—
169C2×Dic86—42no—
170C2×Dic86C22×C412yes—
171C2×Dic86C22×C412yes—
172C2×Dic86#4112yes—
173C2×Dic86#4112yes—
174M16×C43—44no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43C22×C412yes—
186C2×C8×C43C22×C412yes—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—41no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C22⋊Dic43—24no—
194C22⋊Dic43—42no—
195C22⋊Dic43—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43C22×C412yes—
207C4⋊Dic43C22×C412yes—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211Dic43⋊C4—42no—
212C4×Dic43—24no—
213C4×Dic43—42no—
214C4×Dic43—42no—
215C4×Dic43—81no—
216C4×Dic43—81no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43C4×D412yes—
224C23×C43C22×D411yescharacteristic
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
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—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43C4×D412yes—
243C2×C4×C43#13712yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—48no—
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—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275Dic86—22no—
276Dic86—22no—
277Dic86—22no—
278Dic86—22no—
279Dic86—22no—
280Dic86—48no—
281Dic86—41no—
282Dic86—41no—
283Dic86#11714yes—
284C8×C43—22no—
285C8×C43—22no—
286C8×C43—41no—
287C8×C43—41no—
288#22581—431nomaximal, Sylow
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43C2×C4×D411yescharacteristic
297C22×C43#54611yescharacteristic
298C22×C43#54611yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57811yescharacteristic
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43C2×#11711yescharacteristic
309C4×C43#51811yescharacteristic
310C4×C43#55111yescharacteristic
311C4×C43#55111yescharacteristic
312Dic43—24no—
313Dic43—42no—
314Dic43—42no—
315Dic43—42no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319Dic43—81no—
320C2×#419—431no—
321#2347—431no—
322Q8×C22⋊C4—431no—
323#1935—431no—
324#1933—431no—
325#1928—431no—
326#1927—431no—
327#1865—431no—
328#1863—431no—
329#1825—431no—
330#1809—431no—
331#1787—431no—
332#1763—431no—
333C4×#103—431no—
334#1753D4311yescharacteristic
335C2×C43—42no—
336C2×C43#234211yescharacteristic
337C2×C43C4×#13711yescharacteristic
338C2×C43#294711yescharacteristic
339C2×C43#331311yescharacteristic
340C2×C43#332011yescharacteristic
341C2×C43#332611yescharacteristic
342C2×C43#332811yescharacteristic
343C23×Q8—431no—
344C22×M16C2×D4311yescharacteristic
345C2×C4×Q8—431no—
346C2×C4×Q8—431no—
347C2×#117—431no—
348C2×#107—431no—
349C2×#106—431no—
350#419—438no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×C22⋊C8C2×D4311yescharacteristic
360C2×#97C2×D4311yescharacteristic
361C2×C4×C8C2×D4311yescharacteristic
362#391—431no—
363#391—431no—
364#391—861no—
365#391—861no—
366#389—431no—
367#389—431no—
368#388—861no—
369#388—861no—
370#383—861no—
371#380—431no—
372#380—431no—
373#380—861no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4—861no—
377C4×C22⋊C4—861no—
378C4×C22⋊C4C2×D4311yescharacteristic
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#336C2×D4311yescharacteristic
386#336C2×D4311yescharacteristic
387C43#2258111yescharacteristic, complemented, Sylow
388C22×Q8—434no—
389C22×Q8—431no—
390C22×Q8—431no—
391C22×Q8—862no—
392C22×Q8—862no—
393C22×Q8—861no—
394C22×Q8—862no—
395C22×Q8—1721no—
396C22×Q8—1721no—
397C23×C4—861no—
398C23×C4C22×D4311yescharacteristic
399C2×M16—41no—
400C2×M16—41no—
401C2×M16C4×D4314yes—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C4×Q8—862no—
407C4×Q8—862no—
408C4×Q8—1721no—
409C4×Q8—1721no—
410#117—434no—
411#117—862no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4D17211yescharacteristic
426C2×C22⋊C4D17211yescharacteristic
427C2×C42—861no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42C22×D4311yescharacteristic
433C2×C42C22×D4311yescharacteristic
434#107—1721no—
435#106—1721no—
436#103—434no—
437#103—434no—
438#103—434no—
439#103—434no—
440#103—862no—
441#103—862no—
442#103—1721no—
443#103—1721no—
444C22⋊C8—22no—
445#97—41no—
446C4×C8—41no—
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—
456#95—861no—
457#95D17211yescharacteristic
458#95D17211yescharacteristic
459C24C2×D17211yescharacteristic
460C2×Q8—432no—
461C2×Q8—432no—
462C2×Q8—432no—
463C2×Q8—432no—
464C2×Q8—868no—
465C2×Q8—864no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—1722no—
475C2×Q8—1722no—
476C2×Q8—1724no—
477C2×Q8—1724no—
478C2×Q8—1724no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—861no—
484C22×C4—864no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4C2×C4×D4312yes—
495C22×C4C2×D17211yescharacteristic
496C22×C4C2×D17211yescharacteristic
497C22×C4C2×D17211yescharacteristic
498C22×C4C2×D17211yescharacteristic
499C22×C4C2×D17211yescharacteristic
500C22×C4#1062189812yes—
501C22×C4C23×D4311yescharacteristic
502M16—44no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8C2×C4×D4312yes—
514C2×C8C2×C4×D4312yes—
515C4⋊C4—432no—
516C4⋊C4—432no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C4⋊C4—1722no—
530C4⋊C4—1722no—
531C22⋊C4—22no—
532C22⋊C4—41no—
533C22⋊C4—864no—
534C22⋊C4—3441no—
535C22⋊C4—1722no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—864no—
541C42—3441no—
542C42—3441no—
543C42—1722no—
544C42—1722no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23C4×D17212yes—
552C23C22×D17211yescharacteristic
553Q8—434no—
554Q8—862no—
555Q8—862no—
556Q8—862no—
557Q8—862no—
558Q8—862no—
559Q8—1728no—
560Q8—1721no—
561Q8—1721no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
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—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—1728no—
586C2×C4—1721no—
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×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4C4×D17212yes—
605C2×C4#1306335812yes—
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4C2×#1062189811yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337011yescharacteristic
612C8—22no—
613C8—22no—
614C8—41no—
615C8—41no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×C4×D17211yescharacteristic
624C22#1458354411yescharacteristic
625C22#1458354411yescharacteristic
626C22C2×#1306335811yescharacteristic
627C22#1458369911yescharacteristic
628C22#1458371111yescharacteristic
629C22#1458371611yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—864no—
636C4—3441no—
637C4—3441no—
638C4—3441no—
639C4—3441no—
640C4—1722no—
641C4—1722no—
642C4—1722no—
643C4#117×D4311yescharacteristic
644C4#1458337211yescharacteristic
645C4#1458357811yescharacteristic
646C4#1458357811yescharacteristic
647C2—42no—
648C2#1913744711yescharacteristic
649C2C4×#1306335811yescharacteristic
650C2#1914344011yescharacteristic
651C2#1914666311yescharacteristic
652C2#1914676811yescharacteristic
653C2#1914685011yescharacteristic
654C2#1914687911yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1753C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1753D43
hypocenterC43#22581
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
4. #19135285C2semidirect
5. #19135271C2semidirect
6. #19135237C2semidirect
7. #19135230C2semidirect
8. #19134866C2semidirect
9. #19134852C2semidirect
13. #19134426C2semidirect
14. C4×#13063250C2semidirect
22. #14582909C4semidirect
387. C43#22581semidirect

Maximal subgroups

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

subgroupindex
C2×#145829092
#191374862
C22⋊C4×Dic862
#191352852
#191352712
#191352372
#191352302
#191348662
#191348522
#191346912
#191346282
#191345312
#191344262
C4×#130632502
C43×#17532
#2258143