Finite Group Databasebeta

← #25099726

Subgroups — #25099726

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582979C211yesmaximal, characteristic
2#19137234C211yesmaximal, characteristic, complemented
3#19136956C211yesmaximal, characteristic, complemented
4#19135216C211yesmaximal, characteristic, complemented
5#19135214C211yesmaximal, characteristic, complemented
6#19135190C211yesmaximal, characteristic, complemented
7#19135184C211yesmaximal, characteristic, complemented
8#19134943C211yesmaximal, characteristic
9#19134941C211yesmaximal, characteristic
10#19134844C211yesmaximal, characteristic, complemented
11#107×Dic43C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134345C211yesmaximal, characteristic, complemented
15C43×#1862C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20#14582979C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582801C2211yescharacteristic
30#14582800C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582791—21no—
33#14582789—21no—
34#14582761—21no—
35#14582756—21no—
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C22⋊C4×Dic43—21no—
41C22⋊C4×Dic43—21no—
42C4×C22⋊Dic43—21no—
43#14582745C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C4×D43—21no—
64C2×#10621882—22no—
65C2×#10621882—22no—
66C2×#10621882C2×C414yes—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69D4×Dic43—22no—
70D4×Dic43—22no—
71D4×Dic43—22no—
72D4×Dic43C2×C414yes—
73#13063287—22no—
74#13063287C2×C414yescomplemented
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063259—22no—
93#13063258C2×C414yescomplemented
94#13063247—22no—
95#13063247C2×C414yescomplemented
96#13063246—22no—
97#13063245—22no—
98#13063235—22no—
99C8×Dic43C2×C414yescomplemented
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#102×C43—22no—
123#102×C43C2×C414yes—
124#95×C43—21no—
125C24×C43—21no—
126C23×D43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43C22×C412yes—
131C2×D4×C43#4112yes—
132C2×D4×C43#4112yes—
133C22×C4×C43—24no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—81no—
138C22×C4×C43—81no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—24no—
143C22×Dic43—24no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—81no—
148C22×Dic43—81no—
149C22×Dic43—81no—
150C22×Dic43—81no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172C22×C412yes—
161C2×C4×D43—24no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C22×C412yes—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—81no—
175C4⋊C4×C43C22×C412yes—
176C4⋊C4×C43#4112yes—
177C22⋊C4×C43—24no—
178C42×C43—21no—
179C42×C43—21no—
180C22⋊Dic43—24no—
181C22⋊Dic43—24no—
182#10621882—28no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—81no—
185(C2×D43)⋊C4—81no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—81no—
193C4⋊Dic43C22×C412yes—
194C4⋊Dic43#4112yes—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—81no—
198C4×Dic43—81no—
199C4×Dic43—81no—
200C4×Dic43—81no—
201C4×Dic43C22×C412yes—
202C4×Dic43#4112yes—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C22×C412yes—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C22×D411yescharacteristic
217C22×D43—22no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—22no—
227D4×C43#11714yes—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
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×C43—84no—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—84no—
270C2×Dic43—84no—
271C2×Dic43C4×D412yes—
272C2×Dic43C4×D412yes—
273D172—22no—
274D172—22no—
275D172—41no—
276D172—41no—
277C4×D43—84no—
278C8×C43—22no—
279C8×C43—41no—
280C43⋊C8—22no—
281C43⋊C8—41no—
282#21129—431nomaximal, Sylow
283C22×C43—24no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43C2×C4×D411yescharacteristic
291C22×C43#52511yescharacteristic
292C22×C43#52511yescharacteristic
293C22×C43#57611yescharacteristic
294C22×C43#57611yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57811yescharacteristic
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C4×C43—41no—
305C4×C43—42no—
306C4×C43—41no—
307C4×C43—42no—
308C4×C43—81no—
309C4×C43C2×#11711yescharacteristic
310C4×C43C4×#4111yescharacteristic
311C4×C43#52911yescharacteristic
312C4×C43#52911yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—41no—
316Dic43—42no—
317Dic43—41no—
318Dic43—42no—
319Dic43—81no—
320C2×C4×D8—431no—
321#2319—431no—
322#2275—431no—
323#1925—431no—
324#1925—431no—
325#1921—431no—
326#1921—431no—
327#1879—431no—
328#1879—431no—
329#1862—431no—
330#1862D4311yescharacteristic, complemented
331C4×#107—431no—
332#1762—431no—
333#1762—431no—
334#1746—431no—
335C2×C43—44no—
336C2×C43#229011yescharacteristic
337C2×C43#294811yescharacteristic
338C2×C43#295111yescharacteristic
339C2×C43#312211yescharacteristic
340C2×C43#312211yescharacteristic
341C2×C43#312411yescharacteristic
342C2×C43#312411yescharacteristic
343D43—82no—
344C22×D8—431no—
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347C2×C4×D4—431no—
348C2×C4×D4C2×D4311yescharacteristic
349C4×D8—438no—
350C2×#107—431no—
351C2×#107—431no—
352C2×#107C2×D4311yescharacteristic
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102C2×D4311yescharacteristic
358C2×#102C2×D4311yescharacteristic
359C2×#97—431no—
360C2×C4×C8—431no—
361#390—431no—
362#390—431no—
363#389—431no—
364#389C2×D4311yescharacteristic
365#388—861no—
366#388—861no—
367#381—861no—
368#380—861no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C22⋊C4—861no—
374C4×C22⋊C4—861no—
375C4×C22⋊C4—861no—
376#376—431no—
377C2×#95—861no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340C2×D4311yescharacteristic
384#336—431no—
385#336—431no—
386#336—431no—
387#336C2×D4311yescharacteristic
388C43#2112911yescharacteristic, complemented, Sylow
389C22×D4—431no—
390C22×D4C22×D4311yescharacteristic
391C23×C4—21no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C2×D8—434no—
396C2×D8—862no—
397C2×D8—862no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—434no—
405C4×D4—434no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4—862no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42C22×D4311yescharacteristic
433#107—22no—
434#107—434no—
435#107—862no—
436#102—22no—
437#102—434no—
438#102—862no—
439#102—862no—
440#102—862no—
441#102C4×D4314yes—
442#97—862no—
443C4×C8—434no—
444#95—21no—
445#95—431no—
446#95—431no—
447#95—431no—
448#95—431no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—21no—
455C24—861no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—432no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4C2×C4×D4312yes—
466C2×D4#1062190012yes—
467C2×D4#1062190212yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—21no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—864no—
479C22×C4—864no—
480C22×C4—864no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—3441no—
485C22×C4—3441no—
486C22×C4—3441no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493D8—868no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—432no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8C2×C4×D4312yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—81no—
511C4⋊C4—432no—
512C4⋊C4—432no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—3441no—
518C4⋊C4C2×C4×D4312yes—
519C4⋊C4#1062190012yes—
520C22⋊C4—24no—
521C22⋊C4—864no—
522C22⋊C4—864no—
523C22⋊C4—864no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C42—21no—
529C42—21no—
530C42—432no—
531C42—432no—
532C42—861no—
533C42—861no—
534C42—3441no—
535C42—3441no—
536C42—3441no—
537C42—3441no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—862no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23C2×D4×D4311yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—862no—
557D4—862no—
558D4—1721no—
559D4—1721no—
560D4#1306328314yes—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—432no—
578C2×C4—432no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—862no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—3444no—
592C2×C4—3444no—
593C2×C4—3444no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4C2×#1062190011yescharacteristic
605C2×C4C2×#1062190011yescharacteristic
606C2×C4C2×#1062190211yescharacteristic
607C8—22no—
608C8—41no—
609C8—862no—
610C8—1721no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—3441no—
619C22—3441no—
620C22—3441no—
621C22—3441no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22C4×D4×D4311yescharacteristic
626C22#1458340511yescharacteristic
627C22#1458341211yescharacteristic
628C22#1458370011yescharacteristic
629C22#1458370111yescharacteristic
630C22#1458370311yescharacteristic
631C22#1458371511yescharacteristic
632C4—42no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—81no—
637C4—862no—
638C4—862no—
639C4—3441no—
640C4—1722no—
641C4—1721no—
642C4—1722no—
643C4—1721no—
644C4C2×#1306328311yescharacteristic
645C4C4×#1062190011yescharacteristic
646C4#1458342611yescharacteristic
647C4#1458343511yescharacteristic
648C2—44no—
649C2—3442no—
650C2#1913703111yescharacteristic
651C2#1914344211yescharacteristic
652C2#1914346711yescharacteristic
653C2#1914483211yescharacteristic
654C2#1914484011yescharacteristic
655C2#1914485811yescharacteristic
656C2#1914486211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenter#1862D43
hypocenterC43#21129
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #19137234C2semidirect
3. #19136956C2semidirect
4. #19135216C2semidirect
5. #19135214C2semidirect
6. #19135190C2semidirect
7. #19135184C2semidirect
10. #19134844C2semidirect
11. #107×Dic43C2semidirect
12. #19134422C2semidirect
13. #19134419C2semidirect
14. #19134345C2semidirect
15. C43×#1862C2semidirect
20. #14582979C4semidirect
74. #13063287C2×C4semidirect
93. #13063258C2×C4semidirect
95. #13063247C2×C4semidirect
99. C8×Dic43C2×C4semidirect
330. #1862D43semidirect
388. C43#21129semidirect

Maximal subgroups

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

subgroupindex
C2×#145829792
#191372342
#191369562
#191352162
#191352142
#191351902
#191351842
#191349432
#191349412
#191348442
#107×Dic432
#191344222
#191344192
#191343452
C43×#18622
#2112943