Finite Group Databasebeta

← #25104705

Subgroups — #25104705

Order 11008.

826 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583259C211yesmaximal, characteristic
2#19137341C211yesmaximal, characteristic, complemented
3#19137303C211yesmaximal, characteristic
4#19135555C211yesmaximal, characteristic, complemented
5#19135404C211yesmaximal, characteristic
6#19135290C211yesmaximal, characteristic
7#19135283C211yesmaximal, characteristic, complemented
8#19135276C211yesmaximal, characteristic
9#19135269C211yesmaximal, characteristic, complemented
10#19134424C211yesmaximal, characteristic, complemented
11#19134419C211yesmaximal, characteristic
12#19134414C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic
14#19134283C211yesmaximal, characteristic, complemented
15C43×#1836C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×#13063313C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20#14583259C418yescomplemented
21C2×#13063250C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582803—21no—
36#14582803—21no—
37#14582800C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582789—21no—
41#14582789—21no—
42#14582784—21no—
43#14582784—21no—
44#14582770—21no—
45#14582770—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48#14582745C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#97×C43C2211yescharacteristic
54C43×#384C2211yescharacteristic
55C43×#382C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86—21no—
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063325—22no—
67#13063325C2×C414yescomplemented
68#13063313—22no—
69#13063313C2×C414yes—
70#13063290—22no—
71#13063290—22no—
72#13063287—22no—
73#13063287—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063250C2×C414yescomplemented
91#13063250C2×C414yescomplemented
92#13063248—22no—
93#13063248—22no—
94#13063247C2×C414yes—
95#13063247C2×C414yes—
96#13063245—22no—
97#13063245—22no—
98#13063235—22no—
99#13063235—22no—
100C4×C43⋊C8—22no—
101C8×Dic43—22no—
102C8×Dic43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#97×C43C2×C414yescomplemented
123#95×C43—21no—
124#95×C43—21no—
125C23×D43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172C22×C412yes—
146C2×C4×D43—42no—
147C2×C4×D43—81no—
148C2×C4×D43—81no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—24no—
155C2×Dic86—81no—
156C2×Dic86—81no—
157C2×Dic86C22×C412yes—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C412yes—
163C2×C8×C43C22×C412yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—81no—
173C4⋊C4×C43—81no—
174C42×C43C22×C412yes—
175C42×C43#4112yes—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—81no—
180(C2×D43)⋊C4—81no—
181C4⋊Dic43—24no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C412yes—
185C4⋊Dic43C22×C412yes—
186Dic43⋊C4—42no—
187Dic43⋊C4—81no—
188Dic43⋊C4—81no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—42no—
192C4×Dic43—81no—
193C4×Dic43—81no—
194C4×Dic43#4112yes—
195C4×Dic43#4112yes—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8#4112yes—
201C2×C43⋊C8#4112yes—
202C23×C43C22×D411yescharacteristic
203C22×D43—22no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43C4×D412yes—
227C2×C4×C43C4×D412yes—
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43#12412yes—
254C2×Dic43#12412yes—
255D172—22no—
256D172—22no—
257D172—41no—
258D172—41no—
259C4×D43—84no—
260Dic86—22no—
261Dic86—22no—
262Dic86—41no—
263Dic86—41no—
264Dic86—84no—
265C8×C43—22no—
266C8×C43—22no—
267C43⋊C8—22no—
268C43⋊C8—22no—
269#21654—431nomaximal, Sylow
270C22×C43C2×C4×D411yescharacteristic
271C22×C43C2×#12411yescharacteristic
272C22×C43#53211yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57711yescharacteristic
276C22×C43#57811yescharacteristic
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43C4×#4111yescharacteristic
291C4×C43C4×#4111yescharacteristic
292C4×C43#52911yescharacteristic
293C4×C43#52911yescharacteristic
294Dic43—22no—
295Dic43—22no—
296Dic43—41no—
297Dic43—41no—
298Dic43—42no—
299Dic43—42no—
300Dic43—42no—
301C2×#489—431no—
302#2331—431no—
303#2326—431no—
304#1990—431no—
305#1958—431no—
306#1936—431no—
307#1935—431no—
308#1934—431no—
309#1933—431no—
310#1836D4311yescharacteristic, complemented
311#1763—431no—
312#1762—431no—
313C4×#103—431no—
314C4×#102—431no—
315#1726—431no—
316C2×C43C4×#12411yescharacteristic
317C2×C43#294611yescharacteristic
318C2×C43#294711yescharacteristic
319C2×C43#313611yescharacteristic
320C2×C43#313711yescharacteristic
321C2×C43#317311yescharacteristic
322C2×C43#317511yescharacteristic
323D43—82no—
324C2×C4⋊Q8—431no—
325C2×#124—431no—
326C2×C4×Q8—431no—
327C2×C4×D4—431no—
328#489—438no—
329C2×#103—431no—
330C2×#103—431no—
331C2×#103—431no—
332C2×#103—431no—
333C2×#102—431no—
334C2×#102—431no—
335C2×#102—431no—
336C2×#102—431no—
337C2×#97—431no—
338C2×#97—431no—
339C2×#97C2×D4311yescharacteristic
340C2×C4×C8—431no—
341C2×C4×C8—431no—
342C2×C4×C8—431no—
343#391—431no—
344#391—861no—
345#391—861no—
346#390—431no—
347#389—431no—
348#389—431no—
349#388—861no—
350#388—861no—
351#387—861no—
352#387—861no—
353#385—861no—
354#385—861no—
355#384C2×D4311yescharacteristic
356#382C2×D4311yescharacteristic
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359#376—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340C2×D4311yescharacteristic
365#340C2×D4311yescharacteristic
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368C43#2165411yescharacteristic, complemented, Sylow
369C22×Q8—431no—
370C22×Q8—861no—
371C22×D4—431no—
372C23×C4—861no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8C22×D4311yescharacteristic
376C22×C8C22×D4311yescharacteristic
377C4⋊Q8—434no—
378C4⋊Q8—862no—
379#124—434no—
380#124—862no—
381C4×Q8—862no—
382C4×Q8—862no—
383C4×D4—862no—
384C4×D4—862no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—861no—
405C2×C42—861no—
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408#103—434no—
409#103—434no—
410#103—862no—
411#103—862no—
412#102—434no—
413#102—434no—
414#102—862no—
415#102—862no—
416#97—862no—
417#97—862no—
418#97C4×D4314yescomplemented
419C4×C8—862no—
420C4×C8—862no—
421C4×C8—862no—
422#95—21no—
423#95—21no—
424#95—431no—
425#95—431no—
426#95—431no—
427#95—431no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—861no—
435C2×Q8—432no—
436C2×Q8—864no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—3441no—
443C2×Q8—3441no—
444C2×D4—432no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—861no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—3441no—
462C22×C4—3441no—
463C22×C4—1722no—
464C22×C4D4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4C23×D4311yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—432no—
472C2×C8—432no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×C4×D4312yes—
478C2×C8C2×C4×D4312yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4—432no—
490C4⋊C4—432no—
491C4⋊C4—864no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—3441no—
495C4⋊C4—3441no—
496C4⋊C4—1722no—
497C22⋊C4—864no—
498C22⋊C4—864no—
499C22⋊C4—3441no—
500C22⋊C4—3441no—
501C22⋊C4—1722no—
502C42—432no—
503C42—432no—
504C42—861no—
505C42—861no—
506C42—3441no—
507C42—3441no—
508C42—1722no—
509C42C2×C4×D4312yes—
510C42#1062190212yes—
511C23—862no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23C2×D4×D4311yescharacteristic
519Q8—862no—
520Q8—862no—
521Q8—3444no—
522Q8—1721no—
523Q8—1721no—
524D4—862no—
525D4—862no—
526D4—1721no—
527D4—1721no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—432no—
545C2×C4—432no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—3444no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4#1306328712yes—
567C2×C4#1306328712yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4#41×D4311yescharacteristic
572C2×C4#41×D4311yescharacteristic
573C2×C4C2×#1062190211yescharacteristic
574C8—22no—
575C8—22no—
576C8—862no—
577C8—862no—
578C22—3441no—
579C22—3441no—
580C22—3441no—
581C22—3441no—
582C22—1722no—
583C22—1722no—
584C22—1722no—
585C22C2×#1306328711yescharacteristic
586C22#124×D4311yescharacteristic
587C22#1458344811yescharacteristic
588C22#1458370311yescharacteristic
589C22#1458370811yescharacteristic
590C22#1458370911yescharacteristic
591C22#1458371511yescharacteristic
592C4—22no—
593C4—22no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—862no—
599C4—862no—
600C4—1722no—
601C4—1722no—
602C4—1721no—
603C4—1722no—
604C4—1721no—
605C4#1458336711yescharacteristic
606C4#1458336711yescharacteristic
607C4#1458343411yescharacteristic
608C4#1458343411yescharacteristic
609C2—3442no—
610C2#1913713411yescharacteristic
611C2#1914342511yescharacteristic
612C2#1914343611yescharacteristic
613C2#1914495011yescharacteristic
614C2#1914496111yescharacteristic
615C2#1914521111yescharacteristic
616C2#1914523311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1836C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1836D43
hypocenterC43#21654
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
2. #19137341C2semidirect
4. #19135555C2semidirect
7. #19135283C2semidirect
9. #19135269C2semidirect
10. #19134424C2semidirect
12. #19134414C2semidirect
14. #19134283C2semidirect
15. C43×#1836C2semidirect
20. #14583259C4semidirect
67. #13063325C2×C4semidirect
90. #13063250C2×C4semidirect
91. #13063250C2×C4semidirect
122. #97×C43C2×C4semidirect
310. #1836D43semidirect
368. C43#21654semidirect
418. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832592
#191373412
#191373032
#191355552
#191354042
#191352902
#191352832
#191352762
#191352692
#191344242
#191344192
#191344142
#191344092
#191342832
C43×#18362
#2165443