Finite Group Databasebeta

← #25196354

Subgroups — #25196354

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140571C211yesmaximal, characteristic, complemented
2#19137318C211yesmaximal, characteristic
3#19136162C211yesmaximal, characteristic, complemented
4#19135830C211yesmaximal, characteristic
5#19135829C211yesmaximal, characteristic
6#19135293C211yesmaximal, characteristic, complemented
7#19135290C211yesmaximal, characteristic, complemented
8#19135279C211yesmaximal, characteristic, complemented
9#19135276C211yesmaximal, characteristic, complemented
10#19134604C211yesmaximal, characteristic, complemented
11#19134604C211yesmaximal, characteristic, complemented
12#19134594C211yesmaximal, characteristic, complemented
13#19134594C211yesmaximal, characteristic, complemented
14#19134451C211yesmaximal, characteristic, complemented
15C43×#2101C211yesmaximal, characteristic, complemented
16C2×#13063322C2211yescharacteristic
17C2×#13063287C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×Dic43⋊C8C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×#13063247C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582840—21no—
32#14582839—21no—
33#14582832—21no—
34#14582830—21no—
35#14582800C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582777—21no—
41#14582777—21no—
42#14582777—21no—
43#14582777—21no—
44#14582768C2211yescharacteristic
45#14582764C2211yescharacteristic
46#14582745C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#382C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063322—22no—
68#13063322—22no—
69#13063287—22no—
70#13063287—22no—
71#13063287—22no—
72#13063287—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
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×(C2×D43)⋊C4—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88Dic43⋊C8—22no—
89Dic43⋊C8—22no—
90#13063247—22no—
91#13063247—22no—
92#13063247—41no—
93#13063247—41no—
94#13063245—22no—
95#13063245—22no—
96#13063245—41no—
97#13063245—41no—
98#13063235—41no—
99C8×Dic43—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43—21no—
121C23×D43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—24no—
138C2×D172—24no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—81no—
148C2×D172—81no—
149C2×D172—81no—
150C2×D172—81no—
151C2×D172#4112yes—
152C2×D172#4112yes—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—81no—
156C2×C4×D43—81no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×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—21no—
173C4⋊C4×C43—81no—
174C42×C43—21no—
175C42×C43—21no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—81no—
179(C2×D43)⋊C4—81no—
180(C2×D43)⋊C4—81no—
181(C2×D43)⋊C4—81no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—81no—
187Dic43⋊C4—81no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43#4112yes—
194C4×Dic43#4112yes—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C23×C43C22×D411yescharacteristic
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43#12412yes—
257C2×Dic43#12412yes—
258D172—22no—
259D172—22no—
260D172—22no—
261D172—22no—
262D172—41no—
263D172—41no—
264D172—41no—
265D172—41no—
266D172—84no—
267D172—84no—
268C4×D43—84no—
269C4×D43—84no—
270C8×C43—41no—
271C8×C43—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274#29133—431nomaximal, Sylow
275C22×C43#52511yescharacteristic
276C22×C43C2×#12411yescharacteristic
277C22×C43#53711yescharacteristic
278C22×C43#57611yescharacteristic
279C22×C43#57611yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57711yescharacteristic
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—42no—
287C2×D43—42no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43#55211yescharacteristic
303C4×C43#55211yescharacteristic
304C4×C43#55311yescharacteristic
305C4×C43#55311yescharacteristic
306Dic43—22no—
307Dic43—22no—
308Dic43—41no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312#2647—431no—
313#2328—431no—
314#2101—431no—
315#2101D4311yescharacteristic, complemented
316#2041—431no—
317#2041—431no—
318#1936—431no—
319#1936—431no—
320#1934—431no—
321#1934—431no—
322#1804—431no—
323#1804—431no—
324#1802—431no—
325#1802—431no—
326#1768—431no—
327C2×C43#256211yescharacteristic
328C2×C43#312211yescharacteristic
329C2×C43#312311yescharacteristic
330C2×C43#313611yescharacteristic
331C2×C43#313611yescharacteristic
332C2×C43#325711yescharacteristic
333C2×C43#325711yescharacteristic
334D43—82no—
335D43—82no—
336C2×#127—431no—
337C2×C4×D4—431no—
338C2×C4×D4—431no—
339C2×C4⋊C8—431no—
340C2×C4⋊C8—431no—
341C2×#102—431no—
342C2×#102—431no—
343C2×#102—431no—
344C2×#102—431no—
345C2×#102—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×#102—431no—
349C2×#97—431no—
350C2×C4×C8—431no—
351#400—861no—
352#400—861no—
353#398—861no—
354#398—861no—
355#390—431no—
356#390—431no—
357#389—431no—
358#389—431no—
359#389—431no—
360#389C2×D4311yescharacteristic
361#386—861no—
362#386—861no—
363#386—861no—
364#386—861no—
365#384—431no—
366#382—431no—
367#382C2×D4311yescharacteristic
368#376—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340C2×D4311yescharacteristic
374#340C2×D4311yescharacteristic
375#340C2×D4311yescharacteristic
376#340C2×D4311yescharacteristic
377#336—431no—
378#336C2×D4311yescharacteristic
379C43#2913311yescharacteristic, complemented, Sylow
380C22×D4—431no—
381C22×D4—431no—
382C22×D4—861no—
383C22×D4—861no—
384C23×C4—861no—
385C23×C4—861no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390#127—862no—
391#127—862no—
392C4×D4—862no—
393C4×D4—862no—
394C4×D4—862no—
395C4×D4—862no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42C22×D4311yescharacteristic
417C4⋊C8—862no—
418C4⋊C8—862no—
419#102—862no—
420#102—862no—
421#102—862no—
422#102—862no—
423#102—1721no—
424#102—1721no—
425#102—1721no—
426#102—1721no—
427#97—1721no—
428C4×C8—1721no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—431no—
433#95—431no—
434#95—431no—
435#95—431no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441C24—861no—
442C24—861no—
443C2×D4—432no—
444C2×D4—432no—
445C2×D4—864no—
446C2×D4—864no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—3441no—
458C2×D4—3441no—
459C2×D4—3441no—
460C2×D4—3441no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—3441no—
472C22×C4—3441no—
473C22×C4—3441no—
474C22×C4—3441no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4C23×D4311yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—81no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—3441no—
506C4⋊C4—3441no—
507C4⋊C4—3441no—
508C4⋊C4—3441no—
509C4⋊C4—3441no—
510C22⋊C4—3441no—
511C22⋊C4—3441no—
512C22⋊C4—3441no—
513C22⋊C4—3441no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C42—21no—
517C42—21no—
518C42—432no—
519C42—432no—
520C42—861no—
521C42—861no—
522C23—862no—
523C23—862no—
524C23—1721no—
525C23—1721no—
526C23—1721no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23—1721no—
535C23—1721no—
536C23C2×D4×D4311yescharacteristic
537D4—862no—
538D4—862no—
539D4—862no—
540D4—862no—
541D4—3444no—
542D4—3444no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546D4—1721no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—432no—
566C2×C4—432no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—3444no—
578C2×C4—3444no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4#41×D4311yescharacteristic
586C2×C4#41×D4311yescharacteristic
587C2×C4#41×D4311yescharacteristic
588C2×C4#41×D4311yescharacteristic
589C2×C4#1306337111yescharacteristic
590C2×C4#1306337311yescharacteristic
591C8—41no—
592C8—41no—
593C8—1721no—
594C8—1721no—
595C22—3441no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—3441no—
600C22—3441no—
601C22—3441no—
602C22—3441no—
603C22—1722no—
604C22—1722no—
605C22—1722no—
606C22—1722no—
607C22—1722no—
608C22—1722no—
609C22#1458340711yescharacteristic
610C22#124×D4311yescharacteristic
611C22#1458347911yescharacteristic
612C22#1458370111yescharacteristic
613C22#1458370311yescharacteristic
614C22#1458370611yescharacteristic
615C22#1458370811yescharacteristic
616C4—41no—
617C4—41no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—862no—
623C4—862no—
624C4—3441no—
625C4—3441no—
626C4—1721no—
627C4—1721no—
628C4#1458358111yescharacteristic
629C4#1458358111yescharacteristic
630C4#1458360011yescharacteristic
631C4#1458360011yescharacteristic
632C2—3442no—
633C2—3442no—
634C2#1913975711yescharacteristic
635C2#1914483411yescharacteristic
636C2#1914484311yescharacteristic
637C2#1914494611yescharacteristic
638C2#1914494811yescharacteristic
639C2#1914601011yescharacteristic
640C2#1914601211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2101C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#2101D43
hypocenterC43#29133
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
1. #19140571C2semidirect
3. #19136162C2semidirect
6. #19135293C2semidirect
7. #19135290C2semidirect
8. #19135279C2semidirect
9. #19135276C2semidirect
10. #19134604C2semidirect
11. #19134604C2semidirect
12. #19134594C2semidirect
13. #19134594C2semidirect
14. #19134451C2semidirect
15. C43×#2101C2semidirect
315. #2101D43semidirect
379. C43#29133semidirect

Maximal subgroups

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

subgroupindex
#191405712
#191373182
#191361622
#191358302
#191358292
#191352932
#191352902
#191352792
#191352762
#191346042
#191345942
#191344512
C43×#21012
#2913343