Finite Group Databasebeta

← #25113928

Subgroups — #25113928

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#19137482C211yesmaximal, characteristic
3#19137427C211yesmaximal, characteristic
4#19135283C211yesmaximal, characteristic, complemented
5#19135269C211yesmaximal, characteristic, complemented
6#19135235C211yesmaximal, characteristic, complemented
7#19135228C211yesmaximal, characteristic, complemented
8#19134860C211yesmaximal, characteristic, complemented
9#19134846C211yesmaximal, characteristic, complemented
10#19134687C211yesmaximal, characteristic
11#19134529C211yesmaximal, characteristic
12#19134424C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic
15C43×#1809C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C2×#13063290C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20#14582909C418yescomplemented
21C2×#13063250C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582804C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582803—21no—
35#14582803—21no—
36#14582795C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582793—21no—
39#14582793—21no—
40#14582763—21no—
41#14582757—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45C4×C22⋊Dic43C2211yescharacteristic
46#14582744—21no—
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
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—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063290—22no—
73#13063290—22no—
74#13063290—41no—
75#13063290—41no—
76#13063284—22no—
77#13063284C2×C414yes—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43D411yescharacteristic
86C2×C22⋊Dic43D411yescharacteristic
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063250C2×C414yes—
95#13063250C2×C414yes—
96#13063250C2×C414yes—
97#13063250C2×C414yes—
98#13063248—22no—
99#13063248—22no—
100#13063248—41no—
101#13063248—41no—
102C22⋊(C43⋊C8)—22no—
103#13063235—41no—
104C8×Dic43—41no—
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⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C2×M16×C43—41no—
117C2×M16×C43—41no—
118C2×M16×C43C2×C414yes—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127#107×C43—41no—
128#106×C43—41no—
129#95×C43—21no—
130#95×C43—21no—
131C24×C43C2×D411yescharacteristic
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43C22×C412yes—
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—42no—
150C22×Dic43—42no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
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×C43C22×C412yes—
180C2×C8×C43C22×C412yes—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C22⋊C4×C43—42no—
190C22⋊C4×C43—81no—
191C22⋊Dic43—22no—
192C22⋊Dic43—24no—
193C22⋊Dic43—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C22×C412yes—
197C4⋊Dic43C22×C412yes—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—81no—
201Dic43⋊C4—81no—
202C4×Dic43—24no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
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—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—41no—
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×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43C4×D412yes—
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—21no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—48no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43#13712yes—
275Dic86—22no—
276Dic86—22no—
277Dic86—22no—
278Dic86—22no—
279Dic86—22no—
280Dic86—48no—
281Dic86—41no—
282Dic86—41no—
283Dic86#11714yes—
284C8×C43—22no—
285C8×C43—22no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288#22585—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—81no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43C2×#11711yescharacteristic
309C4×C43#51811yescharacteristic
310C4×C43#55111yescharacteristic
311C4×C43#55111yescharacteristic
312Dic43—24no—
313Dic43—22no—
314Dic43—41no—
315Dic43—42no—
316Dic43—42no—
317Dic43—42no—
318Dic43—41no—
319Dic43—41no—
320C2×#419—431no—
321#2346—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#1809D4311yescharacteristic
331#1787—431no—
332#1763—431no—
333C4×#103—431no—
334#1753—431no—
335C2×C43—42no—
336C2×C43#234211yescharacteristic
337C2×C43C4×#13711yescharacteristic
338C2×C43#294711yescharacteristic
339C2×C43#331211yescharacteristic
340C2×C43#332111yescharacteristic
341C2×C43#332711yescharacteristic
342C2×C43#332911yescharacteristic
343C23×Q8—431no—
344C22×M16C2×D4311yescharacteristic
345C2×C4×Q8—431no—
346C2×C4×Q8—431no—
347C2×#117—431no—
348C2×#107C2×D4311yescharacteristic
349C2×#106C2×D4311yescharacteristic
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⋊C8—431no—
360C2×#97—431no—
361C2×C4×C8—431no—
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#382—861no—
371#380—861no—
372#380C2×D4311yescharacteristic
373#380C2×D4311yescharacteristic
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C22⋊C4—431no—
377C4×C22⋊C4—861no—
378#376—861no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340C2×D4311yescharacteristic
384#340C2×D4311yescharacteristic
385#336—431no—
386#336—431no—
387C43#2258511yescharacteristic, 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×C8—431no—
403C22×C8—431no—
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—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—431no—
425C2×C22⋊C4—431no—
426C2×C22⋊C4—861no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42—861no—
434#107—41no—
435#106—41no—
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—862no—
445#97—1721no—
446C4×C8—1721no—
447#95—21no—
448#95—21no—
449#95—431no—
450#95—431no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459C24D4×D4311yescharacteristic
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—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—861no—
492C22×C4—864no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—1722no—
497C22×C4—1722no—
498C22×C4C2×C4×D4312yes—
499C22×C4D4×D4311yescharacteristic
500C22×C4#1062190212yes—
501C22×C4C23×D4311yescharacteristic
502M16—44no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8C2×C4×D4312yes—
514C2×C8C2×C4×D4312yes—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—432no—
524C4⋊C4—432no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—3441no—
528C4⋊C4—3441no—
529C4⋊C4—1722no—
530C4⋊C4—1722no—
531C22⋊C4—42no—
532C22⋊C4—81no—
533C22⋊C4—862no—
534C22⋊C4—864no—
535C22⋊C4—1721no—
536C42—864no—
537C42—861no—
538C42—861no—
539C42—861no—
540C42—861no—
541C42—1722no—
542C42—1722no—
543C42—1722no—
544C42—1722no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23#1306328712yes—
552C23C2×D4×D4311yescharacteristic
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—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—432no—
581C2×C4—862no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—1728no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4#1306328712yes—
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4C2×#1062190211yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337011yescharacteristic
612C8—22no—
613C8—22no—
614C8—1721no—
615C8—1721no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×#1306328711yescharacteristic
624C22#1458353811yescharacteristic
625C22#1458353811yescharacteristic
626C22#137×D4311yescharacteristic
627C22#1458369511yescharacteristic
628C22#1458370911yescharacteristic
629C22#1458371511yescharacteristic
630C4—22no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—862no—
636C4—864no—
637C4—1722no—
638C4—1721no—
639C4—1721no—
640C4—1721no—
641C4—1722no—
642C4—1722no—
643C4#117×D4311yescharacteristic
644C4#1458337211yescharacteristic
645C4#1458357611yescharacteristic
646C4#1458357611yescharacteristic
647C2—42no—
648C2#1913744111yescharacteristic
649C2#1914341311yescharacteristic
650C2#1914343611yescharacteristic
651C2#1914664111yescharacteristic
652C2#1914677611yescharacteristic
653C2#1914686911yescharacteristic
654C2#1914688411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1809C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1809D43
hypocenterC43#22585
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
4. #19135283C2semidirect
5. #19135269C2semidirect
6. #19135235C2semidirect
7. #19135228C2semidirect
8. #19134860C2semidirect
9. #19134846C2semidirect
12. #19134424C2semidirect
13. #19134414C2semidirect
20. #14582909C4semidirect
387. C43#22585semidirect

Maximal subgroups

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

subgroupindex
C2×#145829092
#191374822
#191374272
#191352832
#191352692
#191352352
#191352282
#191348602
#191348462
#191346872
#191345292
#191344242
#191344142
#191343762
C43×#18092
#2258543